SBI PO Prelims Memory Based Paper (Held On: 8 March 2025 Shift 3) (Previous Year Paper)

The correct answer is The man and his wife's fight.

Key Points

The use of an apostrophe is used to form possessive nouns.

• ​For example: Eminem's cap, Virat's bat, etc.
• ​When there are two nouns, as given in the question, always use the apostrophe at the last name only.
• Don't use the apostrophe at the first name.
• The use of "The" is necessary here. "The" is a definite article that is used before singular and plural nouns when the noun is specific or particular.
• Thus, the correct answer is: The man and his wife's fight disrupted the sleep of the people early in the morning.

​

Additional Information

The use of an apostrophe is incorrect when it is used with objects.

• For example: Table's leg (incorrect)
• However, an apostrophe is used with time, weight, distance, amount or personified nouns.
• For example: 

The correct answer is neither my brother nor my friends are.

Key Points

Neither...nor is correlative conjunction.

• Correlative conjunctions are always used in pairs.
• In the case of neither...nor, the verb must always agree with the subject which is closest.
• For example: Neither my friends nor I am coming to the party.
• Thus, the correct answer is: I am sorry to say this but neither my brother nor my friends are going to attend your wedding.

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Additional Information

The correct answer is was the better of the two brothers.

Key Points

When one is chosen out of two, we use a comparative degree.

• In phrases like the question, the comparative degree is preceded by "the" and followed by "of".
• For example: Cristiano is the better of the two players.
• Thus, the correct answer is: When the final results came out, it was obvious that Ramesh was the better of the two brothers.

​

Additional Information

When one is chosen out of more than two, we use a superlative degree.

• The superlative degree is preceded by "the" and followed by "of", just like the comparative degree.
• For example: Cristiano is the best of all the players.

The correct answer is 'production'.

 

Key Points

• The passage discusses the decline in the output of rice and millet, referring to the quantity produced.
• The appropriate noun should indicate the overall yield or output, which is directly related to the amount being produced.
• "Production" fits well as it denotes the process and quantity of crops being grown and harvested.
• Other options ("abundance", "consumption", "distribution", "import") do not specifically address the decrease in the creation or growing of these staple crops.

Therefore, the correct answer is 'Option 2'.

 

Complete Passage: Rice and millet are two of the most important staple crops in the world. However, recent studies have shown a significant decline in their production. This decline in production can be attributed to various factors, including climate change, soil degradation, and water scarcity. To address these challenges, countries must come together and work towards sustainable agriculture practices. It is crucial to (B) ________ innovative solutions to enhance crop yield without harming the environment. Collaborative efforts and sharing of resources can lead to (C) ________ results. Additionally, educating farmers about modern farming techniques and providing them with the necessary tools and support is paramount. Such initiatives not only help in improving crop production but also (D) ________ farmers' livelihoods. Governments, NGOs, and the private sector must (E) ________ hands to create policies and programs that are focused on long-term sustainability. By doing so, we can ensure that future generations have access to sufficient food supplies. Ultimately, it is a shared responsibility to (F) ________ our planet while meeting the food demands of a growing population.

 

Additional Information

• Abundance (प्रचुरता): Abundance means a large quantity of something, which does not fit as it does not suggest a decline.
• Consumption (उपभोग): Consumption means using up of resources, which is not related to the decline in the making of crops.
• Distribution (वितरण): Distribution refers to spreading the crop among various buyers and consumers, which is not linked to the decline in growing the crops.
• Import (आयात): Import refers to bringing in goods from another country, which does not fit the context of production within a country.

The correct answer is 'develop'.

 

Key Points

• The passage discusses finding ways to solve the decline in crop production through innovative solutions.
• The appropriate verb should indicate the process of creating or coming up with new solutions.
• "Develop" fits well as it means to create or formulate, which aligns with the need for innovative solutions to improve crop yields.
• Other options ("acknowledge", "discover", "initiate", "implement") do not convey the process of creating innovative solutions.

Therefore, the correct answer is 'Option 5'.

 

Complete Passage: Rice and millet are two of the most important staple crops in the world. However, recent studies have shown a significant decline in their production. This decline in production can be attributed to various factors, including climate change, soil degradation, and water scarcity. To address these challenges, countries must come together and work towards sustainable agriculture practices. It is crucial to develop innovative solutions to enhance crop yield without harming the environment. Collaborative efforts and sharing of resources can lead to (C) ________ results. Additionally, educating farmers about modern farming techniques and providing them with the necessary tools and support is paramount. Such initiatives not only help in improving crop production but also (D) ________ farmers' livelihoods. Governments, NGOs, and the private sector must (E) ________ hands to create policies and programs that are focused on long-term sustainability. By doing so, we can ensure that future generations have access to sufficient food supplies. Ultimately, it is a shared responsibility to (F) ________ our planet while meeting the food demands of a growing population.

 

Additional Information

• Acknowledge (स्वीकार करना): Acknowledge means to accept or admit the existence or truth of something, which does not fit the context of creating solutions.
• Discover (खोज करना): Discover means to find something unexpectedly, which does not align with actively creating new solutions.
• Initiate (प्रारंभ करना): Initiate means to begin or start something, which is not the same as creating new solutions.
• Implement (कार्यान्वयन करना): Implement means to put a plan into action, which is a later step after innovative solutions have been developed.

The correct answer is 'tangible'.

 

Key Points

• The passage mentions that collaborative efforts and sharing of resources will lead to certain results in crop yield and sustainability.
• The appropriate adjective should indicate the kind of results that can be observed and measured.
• "Tangible" fits well as it means something that can be perceived by touch or is clear and definite, which is suitable when discussing observable improvements.
• Other options ("consistent", "variable", "mixed", "negative") do not align with the need for clear and measurable outcomes.

Therefore, the correct answer is 'Option 1'.

 

Complete Passage: Rice and millet are two of the most important staple crops in the world. However, recent studies have shown a significant decline in their production. This decline in production can be attributed to various factors, including climate change, soil degradation, and water scarcity. To address these challenges, countries must come together and work towards sustainable agriculture practices. It is crucial to develop innovative solutions to enhance crop yield without harming the environment. Collaborative efforts and sharing of resources can lead to tangible results. Additionally, educating farmers about modern farming techniques and providing them with the necessary tools and support is paramount. Such initiatives not only help in improving crop production but also (D) ________ farmers' livelihoods. Governments, NGOs, and the private sector must (E) ________ hands to create policies and programs that are focused on long-term sustainability. By doing so, we can ensure that future generations have access to sufficient food supplies. Ultimately, it is a shared responsibility to (F) ________ our planet while meeting the food demands of a growing population.

 

Additional Information

• Consistent (लगातार): Consistent means acting or done in the same way over time, which does not indicate measurable results.
• Variable (परिवर्तनीय): Variable means not consistent or having a fixed pattern, which is not suitable for describing clear outcomes.
• Mixed (मिश्रित): Mixed means having different or opposing elements, which does not align with describing clear and definite results.
• Negative (नकारात्मक): Negative means not desirable or optimistic, which is not suitable for describing positive and clear outcomes in the context of the passage.

The correct answer is 'secure'.

 

Key Points

• The passage emphasizes the importance of improving crop production and the role of initiatives in ensuring farmers' livelihoods.
• The appropriate verb should indicate protecting or ensuring something in the context of farmers' livelihoods.
• "Secure" fits well as it means to make something safe or ensure it is protected, which aligns with the context of safeguarding farmers' livelihoods through the initiatives mentioned.
• Other options ("facilitate", "impact", "diminish", "worsen") do not convey the sense of ensuring or protecting livelihoods.

Therefore, the correct answer is 'Option 5'.

 

Complete Passage: Rice and millet are two of the most important staple crops in the world. However, recent studies have shown a significant decline in their production. This decline in production can be attributed to various factors, including climate change, soil degradation, and water scarcity. To address these challenges, countries must come together and work towards sustainable agriculture practices. It is crucial to develop innovative solutions to enhance crop yield without harming the environment. Collaborative efforts and sharing of resources can lead to tangible results. Additionally, educating farmers about modern farming techniques and providing them with the necessary tools and support is paramount. Such initiatives not only help in improving crop production but also secure farmers' livelihoods. Governments, NGOs, and the private sector must (E) ________ hands to create policies and programs that are focused on long-term sustainability. By doing so, we can ensure that future generations have access to sufficient food supplies. Ultimately, it is a shared responsibility to (F) ________ our planet while meeting the food demands of a growing population.

 

Additional Information

• Facilitate (सुविधाजनक बनाना): Facilitate means to make an action or process easy or easier, which does not convey the sense of ensuring or safeguarding livelihoods.
• Impact (प्रभाव डालना): Impact means to have a strong effect on something, which is not specific to ensuring or protecting livelihoods.
• Diminish (कम करना): Diminish means to make something less or smaller, which is contrary to the idea of protecting livelihoods.
• Worsen (बिगाड़ना): Worsen means to make something worse, which is the opposite of ensuring or safeguarding livelihoods.

The correct answer is 'join'.

 

Key Points

• The passage emphasizes the need for collaboration among governments, NGOs, and the private sector in order to create policies and programs.
• The appropriate verb should indicate working together or coming together.
• "Join" fits well as it means to connect with or come into the company of others for a common purpose, which aligns with the context of creating policies and programs focused on long-term sustainability.
• Other options ("hold", "shake", "combine", "clap") do not convey the sense of working together towards a common goal.

Therefore, the correct answer is 'Option 3'.

 

Complete Passage: Rice and millet are two of the most important staple crops in the world. However, recent studies have shown a significant decline in their production. This decline in production can be attributed to various factors, including climate change, soil degradation, and water scarcity. To address these challenges, countries must come together and work towards sustainable agriculture practices. It is crucial to develop innovative solutions to enhance crop yield without harming the environment. Collaborative efforts and sharing of resources can lead to tangible results. Additionally, educating farmers about modern farming techniques and providing them with the necessary tools and support is paramount. Such initiatives not only help in improving crop production but also secure farmers' livelihoods. Governments, NGOs, and the private sector must join hands to create policies and programs that are focused on long-term sustainability. By doing so, we can ensure that future generations have access to sufficient food supplies. Ultimately, it is a shared responsibility to (F) ________ our planet while meeting the food demands of a growing population.

 

Additional Information

• Hold (पकड़ना): Hold means to have or keep in hand, which does not fit the context of working together.
• Shake (हिलाना): Shake means to move or cause to move up and down or from side to side, which is not related to collaboration.
• Combine (मिलाना): Combine means to join or mix together, but it is not as commonly used with "hands" in the idiomatic expression.
• Clap (ताली बजाना): Clap means to strike the palms of the hands together, which does not convey the sense of joining efforts.

The correct answer is 'nurture'.

 

Key Points

• The passage underscores the importance of protecting our planet and ensuring future food security for the growing population.
• The appropriate verb should convey the idea of caring for and supporting the health of the planet.
• "Nurture" fits well as it means to care for and encourage the growth and development of something, aligning with the context of looking after the planet's well-being.
• Other options ("exploit", "degrade", "abandon", "isolate") do not convey the idea of caring for and protecting the planet.

Therefore, the correct answer is 'Option 1'.

 

Complete Passage: Rice and millet are two of the most important staple crops in the world. However, recent studies have shown a significant decline in their production. This decline in production can be attributed to various factors, including climate change, soil degradation, and water scarcity. To address these challenges, countries must come together and work towards sustainable agriculture practices. It is crucial to develop innovative solutions to enhance crop yield without harming the environment. Collaborative efforts and sharing of resources can lead to tangible results. Additionally, educating farmers about modern farming techniques and providing them with the necessary tools and support is paramount. Such initiatives not only help in improving crop production but also secure farmers' livelihoods. Governments, NGOs, and the private sector must join hands to create policies and programs that are focused on long-term sustainability. By doing so, we can ensure that future generations have access to sufficient food supplies. Ultimately, it is a shared responsibility to nurture our planet while meeting the food demands of a growing population.

 

Additional Information

• Exploit (शोषण करना): Exploit means to make use of something in an unjust or selfish manner, which does not fit the context of caring for the planet.
• Degrade (गिरावट लाना): Degrade means to lower in quality or condition, which is contrary to the goal of protecting the planet.
• Abandon (त्याग देना): Abandon means to leave completely, which does not align with the idea of nurturing the planet.
• Isolate (अलग करना): Isolate means to separate from others, which does not connect with the context of looking after the planet's health.

The correct answer is option 3.

Key Points

To answer this question, first, let's look at the given sentence this way:

Leveraging India's ________ dividend demands a focus on ________ healthcare to ________ the economic and productivity challenges posed by ________ chronic diseases.

• Now, let's understand the meanings of the marked words:
• (A) Widespread - prevalent or occurring over a large area or among many people; common or extensive (व्यापक)
• For Example -
• The widespread use of smartphones has revolutionized communication worldwide.
• (B) Mitigate - to make less severe, serious, or painful; alleviate; lessen the impact or intensity of something (कम करना)
• For Example -
• Planting trees can help mitigate the effects of climate change by absorbing carbon dioxide from the atmosphere.
• (C) Preventive - intended to stop something from happening before it occurs; proactive or precautionary (निवारक)
• For Example -
• Regular exercise and a healthy diet are preventive measures against heart disease.
• (D) Demographic - relating to the characteristics of a population, such as age, gender, income, education, etc. (जनसांख्यिक)
• For Example -
• Advertisers often target their messages based on demographic information to reach their desired audience.
• After understanding the meanings of the marked words, we can conclude that swapping "widespread (A)" with "demographic (D)" and swapping "mitigate (B)" with "preventive (C)" would make the sentence grammatically and contextually correct.
• Here, the word "widespread" (A) refers to something being prevalent over a large area or among many people, while "demographic" (D) relates to characteristics of a population, such as age, gender, income, etc. In the context of the sentence, it makes more sense to refer to the challenges posed by chronic diseases as "widespread" rather than "demographic," as it's the diseases themselves that are widespread, not the characteristics of the population affected by them.
• Also, the word "mitigate" (B) means to make less severe or alleviate, while "preventive" (C) refers to measures taken to stop something from happening before it occurs. In the sentence, it's more appropriate to focus on preventive healthcare to stop or prevent the economic and productivity challenges posed by chronic diseases, rather than trying to mitigate them after they have already occurred.
• Hence, the correct answer is "A-D and B-C."
• The correct sentence after the rearrangement would be: "Leveraging India's demographic dividend demands a focus on preventive healthcare to mitigate the economic and productivity challenges posed by widespread chronic diseases."

The correct answer is option 2.

Key Points

To answer this question, first, let's look at the given sentence this way:

The demographic ________ offers economic growth opportunities, ________ on investments in health, education, and skill development to ________ the working-age population's ________.

• Now, let's understand the meanings of the marked words:
• (A) Dividend - a benefit or advantage gained from an investment or action, typically in the form of profits or returns (लाभ)
• For Example -
• Investing in renewable energy can result in a dividend of cleaner air and reduced carbon emissions.
• (B) Harness - to utilize or control something, typically a resource or energy, productively or efficiently (प्रयोग करना)
• For Example -
• The team worked together to harness the river's power for electricity generation.
• (C) Contingent - dependent on certain conditions or events; liable to occur but not certain (आश्रित)
• For Example -
• The success of the project was contingent on securing funding from investors.
• (D) Potential - the inherent capacity or ability for growth, development, or success (संभावित)
• For Example -
• The young artist showed great potential, with her paintings attracting attention from galleries.
• After understanding the meanings of the marked words, we can conclude that, in the given sentence, swapping "harness (B)" and "contingent (C)" would make the sentence more coherent and contextually correct. "Harness" means to utilize or control something productively or efficiently, typically a resource or energy. In the context of the sentence, it doesn't make sense for economic growth opportunities to "harness" on investments. Instead, it should be contingent on investments, meaning dependent on or influenced by investments.
• Hence, the correct answer is "B-C."
• The correct sentence after the rearrangement would be: "The demographic dividend offers economic growth opportunities, contingent on investments in health, education, and skill development to harness the working-age population's potential."

The correct answer is option 1.

Key Points

To answer this question, first, let's look at the given sentence this way:

Reality shows ________ emotions for profit, ________ perceptions of the real world, and ________ youth to seek ________ human connection amidst the chaos.

• Now, let's understand the meanings of the marked words:
• (A) Genuine - truly what something is said to be; authentic; sincere (वास्तविक)
• For Example -
• Her smile was genuine, expressing her true happiness.
• (B) Distorting - twisting or misrepresenting information, facts, or reality (विकृत)
• For Example -
• Her biased perspective is distorting the reality of the situation.
• (C) Urging - strongly recommending or advocating for something; pressing or pushing for action (प्रेरित)
• For Example -
• She kept urging her friend to try the new restaurant in town because she loved the food there.
• (D) Exploit - to make full use of and derive benefit from something, often unfairly or selfishly (शोषण)
• For Example -
• The company's marketing team devised a plan to exploit social media trends.
• After understanding the meanings of the marked words, we can conclude that in the given sentence, swapping "exploit (D)" and "genuine (A)" would make the sentence more coherent and contextually correct. In the original sentence, the phrase "Reality shows genuine emotions for profit" doesn't align with the context. It implies that reality shows display sincere or authentic emotions solely for profit, which is contradictory. On the other hand, swapping "genuine" with "exploit" would create a more logical and coherent sentence, indicating that reality shows exploit emotions for profit, which is more consistent with their nature and the logical flow of the sentence.
• Hence, the correct answer is "D-A."
• The correct sentence after the rearrangement would be: "Reality shows exploit emotions for profit, distorting perceptions of the real world, and urging youth to seek genuine human connection amidst the chaos."

The correct answer is option 4.

Key Points

To answer this question, first, let's look at the given sentence this way:

Minimalism advocates intelligent choices, ________ living spaces, and ________ necessities over ________, leading to a more ________ and eco-friendly lifestyle.

• Now, let's understand the meanings of the marked words:
• (A) Prioritizing - deciding or organizing in terms of relative importance or urgency (प्राथमिकता देना)
• For Example -
• Prioritizing tasks helps in managing time effectively and meeting deadlines.
• (B) Decluttering - removing unnecessary items or elements from a space or situation (अनावश्यक सामग्री को हटाना)
• For Example -
• Decluttering your desk can enhance productivity by creating a clean and organized workspace.
• (C) Content - experiencing satisfaction, happiness, or peace (संतुष्ट)
• For Example -
• After completing her project, she felt content with her achievements.
• (D) Extravagance - excessive or unnecessary expenditure or outlay of money, time, or resources (अत्यधिकता)
• For Example -
• Their wedding was marked by extravagance, with lavish decorations and gourmet meals.
• After understanding the meanings of the marked words, we can conclude that, in the given sentence, swapping "decluttering (B)" and "prioritizing (A)" and swapping "extravagance (D)" and "content (C)" would make the sentence grammatically and contextually coherent as "decluttering" refers to removing unnecessary items, which should logically come after "prioritizing" since one would prioritize necessities before deciding what to declutter. Also, "extravagance" refers to excessive or unnecessary expenditure or outlay of money, time, or resources. Swapping it with "content" helps maintain the flow and coherence of the sentence, as it contrasts prioritizing necessities over extravagance with leading to a more content lifestyle.
• Hence, the correct answer is "B-A and D-C."
• The correct sentence after the rearrangement would be: "Minimalism advocates intelligent choices, decluttering living spaces, and prioritizing necessities over extravagance, leading to a more content and eco-friendly lifestyle."

The correct answer is Option 1.

 

Key Points

• The paragraph begins by introducing the idea of visiting sites associated with death, disaster, and suffering becoming more popular, with Chernobyl being a prominent destination.
• Sentence C is the first sentence as it introduces the topic:
• "The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations."
• Sentence E follows as it describes what a visit to Chernobyl entails:
• "A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time."
• Sentence D is the third sentence because it provides more detail about what visitors see:
• "The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay."
• Sentence A is the fourth as it highlights the information provided to visitors:
• "Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination."
• The final sentence, B, emphasizes the importance of safety:
• "Safety remains a top priority for those visiting Chernobyl."
• The correct sequence is CEDAB.

 

Coherent paragraph after rearrangement:

"The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations. A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time. The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay. Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination. Safety remains a top priority for those visiting Chernobyl."

The correct answer is Option 5.

 

Key Points

• The paragraph begins by introducing the idea of visiting sites associated with death, disaster, and suffering becoming more popular, with Chernobyl being a prominent destination.
• Sentence C is the first sentence as it introduces the topic:
• "The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations."
• Sentence E follows as it describes what a visit to Chernobyl entails:
• "A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time."
• Sentence D is the third sentence because it provides more detail about what visitors see:
• "The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay."
• Sentence A is the fourth as it highlights the information provided to visitors:
• "Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination."
• The final sentence, B, emphasizes the importance of safety:
• "Safety remains a top priority for those visiting Chernobyl."
• The correct sequence is CEDAB.

 

Coherent paragraph after rearrangement:

"The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations. A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time. The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay. Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination. Safety remains a top priority for those visiting Chernobyl."

The correct answer is Option 1.

 

Key Points

• The paragraph begins by introducing the idea of visiting sites associated with death, disaster, and suffering becoming more popular, with Chernobyl being a prominent destination.
• Sentence C is the first sentence as it introduces the topic:
• "The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations."
• Sentence E follows as it describes what a visit to Chernobyl entails:
• "A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time."
• Sentence D is the third sentence because it provides more detail about what visitors see:
• "The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay."
• Sentence A is the fourth as it highlights the information provided to visitors:
• "Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination."
• The final sentence, B, emphasizes the importance of safety:
• "Safety remains a top priority for those visiting Chernobyl."
• The correct sequence is CEDAB.

 

Coherent paragraph after rearrangement:

"The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations. A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time. The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay. Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination. Safety remains a top priority for those visiting Chernobyl."

The correct answer is Option 4.

 

Key Points

• The paragraph begins by introducing the idea of visiting sites associated with death, disaster, and suffering becoming more popular, with Chernobyl being a prominent destination.
• Sentence C is the first sentence as it introduces the topic:
• "The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations."
• Sentence E follows as it describes what a visit to Chernobyl entails:
• "A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time."
• Sentence D is the third sentence because it provides more detail about what visitors see:
• "The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay."
• Sentence A is the fourth as it highlights the information provided to visitors:
• "Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination."
• The final sentence, B, emphasizes the importance of safety:
• "Safety remains a top priority for those visiting Chernobyl."
• The correct sequence is CEDAB.

 

Coherent paragraph after rearrangement:

"The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations. A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time. The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay. Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination. Safety remains a top priority for those visiting Chernobyl."

The correct answer is Option 2.

 

Key Points

• The paragraph begins by introducing the idea of visiting sites associated with death, disaster, and suffering becoming more popular, with Chernobyl being a prominent destination.
• Sentence C is the first sentence as it introduces the topic:
• "The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations."
• Sentence E follows as it describes what a visit to Chernobyl entails:
• "A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time."
• Sentence D is the third sentence because it provides more detail about what visitors see:
• "The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay."
• Sentence A is the fourth as it highlights the information provided to visitors:
• "Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination."
• The final sentence, B, emphasizes the importance of safety:
• "Safety remains a top priority for those visiting Chernobyl."
• The correct sequence is CEDAB.

 

Coherent paragraph after rearrangement:

"The practice of visiting sites associated with death, disaster, and suffering has seen a rise in popularity over the years, with Chernobyl being one of the most prominent destinations. A visit to Chernobyl provides an eerie yet fascinating look into a place frozen in time. The nearby town of Pripyat, once home to nearly 50,000 people, stands as a ghost town, its buildings abandoned and left to decay. Visitors are often briefed on the heroic efforts of the “liquidators,” the brave men and women who worked tirelessly to contain the radioactive contamination. Safety remains a top priority for those visiting Chernobyl."

The correct answer is Option 1.

 

Key Points

• The passage mentions that the curated gift boxes have been met with considerable success.
• These boxes combine toys, accessories, and apparel, making them a preferred choice for parents.
• The analysis suggests that this segment holds considerable potential for future growth, particularly with the increasing trend of personalized gifting.

Therefore, the correct answer is Option 1.

 

Additional Information

• Children’s earrings: Although they have seen significant growth, the passage specifically highlights the curated gift boxes as having greater future potential.
• Themed clothing: This segment is popular but not specifically mentioned as holding the most future growth potential.
• Toys: Originally the company's main product, but the focus has shifted to more diversified products, including curated gift boxes.
• Seasonal items: The passage mentions sales increase during festive seasons, but it does not focus on them for future growth.

The correct answer is Option 2.

 

Key Points

• Statement A: The company has always focused on apparel and jewellery.
• This statement is incorrect as the passage mentions that the company was originally recognized as a toymaker and has only recently diversified into apparel and jewellery.
• Statement B: Children's earrings and other jewellery have become a significant part of the company’s revenue.
• This statement is correct as the passage states that the sales of children's earrings and other jewellery have seen a significant swell, contributing substantially to the company's revenue.
• Statement C: The themed clothing line has not been successful for Company X.
• This statement is incorrect as the passage mentions that the company's line of themed clothing for children has proven particularly popular.

Therefore, the correct answer is: Only B.

The correct answer is Option 1.

 

Key Points

• Statement A: Company X's sales have been stable throughout the year.
• This statement is incorrect since the passage mentions that sales have seen a consistent increase, especially during festive seasons and school holidays, implying that sales are not stable throughout the year.
• Statement B: Company X has achieved brand recognition among its target audience.
• This statement is correct as the passage mentions the company has strong brand recognition among its target audience.
• Statement C: The company needs to improve its distribution capabilities.
• This statement is correct as the passage indicates the company's current warehouse and logistical capacities are nearing their limits.

Therefore, the correct answer is: Only A.

The correct answer is Option 4.

 

Key Points

• Statement A: Company X's warehouse and logistics capacities are currently more than sufficient.
• This statement is incorrect as the passage states that the current warehouse and logistical capacities are nearing their limits.
• Statement B: The company has made significant strides during festive seasons and school holidays.
• This statement is correct as the analysis indicates a consistent increase in sales, especially during festive seasons and school holidays.
• Statement C: The themed clothing line has proven popular with children.
• This statement is correct as it is mentioned that the company's line of themed clothing for children is particularly popular.

Therefore, the correct answer is: B and C.

The correct answer is Option 1.

 

Key Points

• Statement A: Company X has expanded into new international markets.
• This statement is incorrect as the passage indicates that Company X plans to explore new international markets but has not confirmed expansion into them yet.
• Statement B: The curated gift boxes are preferred by parents for their convenience.
• This statement is correct as mentioned in the passage, the gift boxes have become a preferred choice for parents due to their convenience.
• Statement C: Company X originally focused on making toys.
• This statement is correct as the passage refers to Company X being originally recognized as a toymaker.

Therefore, the correct answer is: Only A.

The correct answer is 'Option 2'.

 

Key Points

• A) Company X's success is solely attributed to its toy line.
• This cannot be inferred from the passage. The passage indicates that Company X has diversified its product lines beyond toys, contributing to overall success.
• B) The company’s focus on a single product line would likely result in revenue fluctuations.
• This can be inferred from the passage. The passage mentions that diversification into other products has provided a stable revenue stream, mitigating seasonal fluctuations often seen in the toy industry.
• C) There is no significant competition in the children’s jewellery sector.
• This cannot be inferred from the passage. The passage mentions that the company faces stiff competition in the jewellery sector.
• D) Themed clothing did not contribute to revenue growth.
• This cannot be inferred from the passage. The passage states that themed clothing for children has proven particularly popular and contributed to revenue growth.
• E) All future growth will come from the international market.
• This cannot be inferred from the passage. While the passage mentions exploring new international markets, it also discusses expanding the online presence and optimizing supply chains as other growth strategies.

Therefore, the correct answer is Option 2.

 

Additional Information

• Only A: Incorrect because A cannot be inferred from the passage.
• Only B: Correct because B can be inferred from the passage.
• All A, B, and C: Incorrect because A and C cannot be inferred from the passage.
• Only C: Incorrect because C cannot be inferred from the passage.

The correct answer is 'adapt and diversify'.

 

Key Points

• The phrase "adapt and diversify" means to adjust to new conditions and to develop a varied range of products or interests. (अनुकूलन और विविधता)
• Company X's ability to adapt and diversify has allowed it to expand into new market segments.
• The other options: "stabilize and identify," "reduce and localize," "innovate and stagnate," and "develop and quantify" do not fit the context as appropriately.

​Therefore, the correct answer is 'Option 3'.

Complete Sentence: The firm's ability to adapt and diversify, coupled with its strong brand recognition among its target audience, positions it for continued growth.

Additional Information

• Stabilize and identify: Stabilizing means making stable, and identifying means recognizing or distinguishing.
• Reduce and localize: Reducing means making smaller or less in amount, and localizing means restricting to a particular place.
• Innovate and stagnate: Innovating means introducing new ideas, and stagnating means ceasing to develop.
• Develop and quantify: Developing means growing or causing to grow, and quantifying means expressing or measuring the quantity of something.

The correct answer is: Option 2 i.e., surge.

Key Points

• The word "swell" in the context of the passage refers to an increase or rise in quantity or volume. (उभार)
• Example: There was a swell in sales during the holiday season.
• The word "surge" refers to a sudden powerful forward or upward movement, often relating to an increase. (लहर)
• Example: We experienced a surge in customer inquiries after the ad campaign.
• Hence, in this context, the word "swell" is similar in meaning to "surge."

Therefore, the correct answer is: surge.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Decrease (कमी): To make or become smaller or fewer in size, amount, intensity, or degree.
• Example: There was a decrease in revenue last quarter.
• Stabilize (स्थिर करना): To make or become unlikely to change, fail, or decline.
• Example: The government took measures to stabilize the economy.
• Compress (संपीडित): To press or squeeze together to reduce in size or volume.
• Example: The data was compressed to save storage space.
• Diminish (घटाना): To make or become less.
• Example: The returns on the investment began to diminish over time.

The correct answer is Option 1.

 

Key Points

• In the passage, the phrase "expand its distribution space" refers to increasing the company's warehousing and logistical capacity to meet growing demand.
• Here, "space" denotes capacity or room for expansion, particularly in terms of storage and distribution infrastructure.
• "Expansion" is the closest in meaning because it reflects the idea of increasing available capacity to support future growth.
• Thus, Option 1 best matches the contextual meaning of "space" in the passage.

Therefore, the correct answer is Expansion.

 

Additional Information

• Option 2: "Deficiency" – Means a lack or shortage, which does not convey the idea of storage or distribution capacity.
• Option 3: "Concession" – Means a compromise or something granted, which is unrelated to the context.
• Option 4: "Limitation" – Means a restriction or constraint. Although limited space is mentioned, this is not the meaning of the word "space" itself.
• Option 5: "Interval" – Means a period of time or a gap between events, which is unrelated to the context of warehousing and logistics.

The correct answer is: Option 5 i.e., company.

Key Points

• The word "firm" in the context of the passage refers to a business or company. (कंपनी)
• Example: The firm has been in business for over 50 years.
• In contrast, the word "company" also refers to a business organization. (कंपनी)
• Example: She works for a tech company that designs software solutions.
• Hence, in the context of the passage, the word "firm" is synonymous with "company."

Therefore, the correct answer is: company.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Unstable (अस्थिर): Not stable; likely to change or fall.
• Example: The stock market is very unstable right now.
• Soft (नरम): Easy to mold, cut, compress, or fold; not hard or firm to the touch.
• Example: She prefers to sleep on a soft pillow.
• Resolute (दृढ़): Admirably purposeful, determined, and unwavering.
• Example: She was resolute in her decision to pursue higher education.
• Temporary (अस्थायी): Lasting for only a limited period of time; not permanent.
• Example: They had to find temporary shelter after their house was flooded.

The correct answer is DABEC.

Key Points Let's consider A, B, C, D, and E to be five blanks, with A being the first B second, and so on.

• The first blank requires a noun and that too a 'living noun' that can speak. Therefore, 'agent' is the correct answer here.
• The second blank requires a noun which is the way of transportation. Therefore, 'bus' is the correct answer here.
• The third blank requires a noun and an adjective will be grammatically incorrect here. so, 'way' is the correct answer here.
• The fourth blank requires a verb as in describing the action. Therefore 'went' is the correct answer.
• The fifth blank requires an adjective describing 'characteristic of the way of transport'. Therefore, 'faster' is the correct answer and seems to be grammatically correct.

Therefore, the correct answer is,

The travel agent said that traveling by bus was the cheapest way, but we went by plane because it was faster

The correct answer is EDACB.

Key Points

Let's consider A, B, C, D, and E to be five blanks, with A being the first B second, and so on.

• The first blank requires a verb as a house is an inanimate object and 'I am house ' is incorrect. Therefore, 'having' is the correct answer here.
• The second blank requires a noun as in ' big what?'- party. Therefore, 'party' is the correct answer here.
• The third blank requires a noun that will denote a place of the party. so, 'house' is the correct answer here.
• The fourth blank requires a verb as in describing the action. Therefore 'inviting' is the correct answer.
• The fifth blank requires a noun for which the adjective 'close' is used. Therefore, 'friends' is the correct answer and seems to be grammatically correct.

Therefore, the correct answer is,

I am having a big party next week at my house and I am inviting all my close friends

The correct answer is CDBEA​.

Key Points 

Let's consider A, B, C, D, and E to be five blanks, with A being the first B second, and so on.

• The first blank requires a noun that too a name of a bird which is mentioned later in the sentence. Therefore, 'woodpecker is the correct answer here
• The second blank requires an adjective which is modifying the noun 'bird'. Therefore, 'small' is the correct answer here.
• The third blank requires a noun that is used for 'feathers' later in the sentence. Therefore, 'bunch' is the correct answer here.
• The fourth blank requires an adjective which is showing the characteristics of the 'feathers'. Therefore 'red' is the correct answer.
• The fifth blank requires a noun to show the place where the bird has feathers. Therefore, 'head' is the correct answer

Therefore, the correct answer is,

A woodpecker is a small bird with a bunch of red feathers on its head.

The correct answer is DCAEB​.

 Key Points

Let's consider A, B, C, D, and E to be five blanks, with A being the first B second, and so on.

• The first blank and the second blank requires two nouns that have specific meanings and are one of a kind because the preposition 'the' is used before them. Therefore in the first blank 'God' and in the second blank 'earth' is the correct answer.
• The third blank requires a verb, which describes the action taking place on the noun 'plants'. Therefore, 'grew' is the correct answer here.
• The fourth blank requires an adjective that describes the noun earth further. Therefore 'populated' is the correct answer.
• The fifth blank requires a preposition and 'with' seems to be grammatically correct here. Therefore, 'with' is the correct answer

Therefore, the correct answer is,

God created the earth from the lower part, grew plants on it, and populated it with animals.

The correct answer is 'Exhort.'

Key Points

• Exhort means to strongly encourage or urge someone to do something.​
• In the first sentence, filling the blank with 'exhort' would imply doctors strongly encourage their patients for regular checkups.
• In the second sentence, filling the blank with 'exhort' would imply that the purpose of commercials is to encourage customers to buy products.
• Therefore, the most appropriate word to be filled in the blank is 'exhort'.

Hence, the correct answer is option 1.

Complete Sentences:

1. Most doctors will exhort their patients to obtain regular check-ups so that they can avoid serious illnesses.
2. The purpose of most commercials is to exhort consumers to buy a particular product or service.

Additional Information

• Let us explore the other options:
• Discourage means to stop somebody from doing something.
• Restrain means to keep someone or something under control or within limits.
• Inhibit means to prevent or prohibit someone from doing something.
• Curb means to limit or control something.

The correct answer is 'Inane.'

Key Points

• Inane means lacking sense, silly.​
• In the first sentence, filling the blank with 'inane' would imply that eating plastic fruit is silly or foolish.
• In the second sentence, filling the blank with 'inane' would imply ignoring silly people or their comments.
• Therefore, the most appropriate word to be filled in the blank is 'inane'.

Hence, the correct answer is option 3.

Complete Sentences:

1. Her idea about eating plastic fruit is totally inane.
2. My teacher is really good about ignoring inane comments from the clowns in our class.

Additional Information

• Let us explore the other options:
• Sensible means (used about people and their behaviour) able to make good judgements based on reason and experience.
• Appreciable means large or important enough to be noticed.
• Audible means able to be heard.
• Visible means able to be seen.

The correct answer is 'Rogue.'

Key Points

• Rogue means a dishonest or unprincipled individual.​
• In the first sentence, filling the blank with 'rogue' would imply the dishonesty of a man who mislead or cheated an old lady.
• In the second sentence, filling the blank with 'rogue' would imply the dishonesty of a narcotics officer.
• Therefore, the most appropriate word to be filled in the blank is 'rogue'.

Hence, the correct answer is option 2.

Complete Sentences:

1. The devilish rogue laughed after he conned the widow out of her savings.
2. The district attorney filed charges against the rogue narcotics officer for collusion with the drug traffickers.

Additional Information

• Let us explore the other options:
• Decent means honest and fair; treating people with respect.
• Ethical means morally good or correct.
• Scrupulous means careful to do what is right or honest.
• Honest means not lying to people or stealing.

The correct answer is option 3.

Key Points

To answer this question, let's break down each sentence to identify the grammatically and contextually correct ones:

• 1) The data shows a significant increase in customer satisfaction.
• This sentence describes the data indicating an increase in customer satisfaction.
• This sentence is grammatically and contextually correct.
• 2) The company's new policy affects all employees immediately.
• This sentence explains the impact of a company's new policy.
• This sentence is grammatically and contextually correct.
• 3) There is less people attending the lecture than expected.
• This sentence discusses the attendance at a lecture.
• The sentence is erroneous because "less" should be "fewer" when referring to countable nouns like "people."
• The correct sentence would be: "There are fewer people attending the lecture than expected."
• 4) She runs more quickly than anyone else on the team.
• This sentence compares someone's running speed to others on the team.
• This sentence is grammatically and contextually correct.
• So, out of the given sentences, only sentence 3 is erroneous.
• Therefore, the correct answer is "option 3."

The correct answer is option 2.

Key Points

To answer this question, let's break down each sentence to identify the grammatically and contextually correct ones:

• 1. The committee members meet every Wednesday to discuss new proposals.
• This sentence describes the regular meetings of the committee members.
• This sentence is grammatically and contextually correct.
• 2. The information you provided are very helpful for our research.
• This sentence describes the usefulness of the information provided.
• The sentence is erroneous because "information" is an uncountable noun and should be followed by "is" instead of "are".
• The correct sentence would be: "The information you provided is very helpful for our research."
• 3. He has a natural talent for drawing and painting.
• This sentence describes someone's natural talent.
• This sentence is grammatically and contextually correct.
• 4. The weather tomorrow is expected to be sunny with a chance of rain in the afternoon.
• This sentence describes a weather forecast.
• This sentence is grammatically and contextually correct.
• 5. All are correct.

So, out of the given sentences, only sentence 2 is erroneous.

Therefore, the correct answer is "option 2."

The correct answer is option 2.

Key Points

To answer this question, let's break down each sentence to identify the grammatically and contextually correct ones:

• 1) Her singing is absolutely beautiful.
• This sentence describes the quality of someone's singing.
• This sentence is grammatically and contextually correct.
• 2) The student were excited about the upcoming holidays.
• This sentence describes students' excitement about holidays.
• This sentence is erroneous because "student" should be plural ("students") to agree with the verb "were."
• The correct sentence would be: "The students were excited about the upcoming holidays."
• 3) The book on the table belongs to John.
• This sentence indicates possession of a book.
• This sentence is grammatically and contextually correct.
• 4) They have decided to sell their house and move abroad.
• This sentence describes a decision to sell a house and relocate.
• This sentence is grammatically and contextually correct.

So, out of the given sentences, option 2 is grammatically incorrect.

The correct answer is option 2.

Key Points

To answer this question, let's break down each sentence to identify the grammatically and contextually correct ones:

• 1) The experiment yielded unexpected results, which were analyzed further.
• This sentence describes the outcome of an experiment and subsequent actions.
• This sentence is grammatically and contextually correct.
• 2) John and Sarah is going to the concert together.
• This sentence describes two people going to a concert.
• The sentence is erroneous because the subject "John and Sarah" is plural and should be followed by "are" instead of "is."
• The correct sentence would be: "John and Sarah are going to the concert together."
• 3) The shop offers a variety of organic products.
• This sentence describes a shop's offerings.
• This sentence is grammatically and contextually correct.
• 4) She always finishes her work before the deadline.
• This sentence describes someone's punctuality with work.
• This sentence is grammatically and contextually correct.
• So, out of the given sentences, only sentence 2 is erroneous.
• Therefore, the correct answer is "option 2."

The correct answer is option 2.

Key Points

To answer this question, let's break down each sentence to identify the grammatically and contextually correct ones:

• 1) He quickly realized that he had made a mistake.
• This sentence describes a person's realization of their error.
• This sentence is grammatically and contextually correct.
• 2) She enjoys hiking, swimming, and to ride horses.
• This sentence lists activities that someone enjoys.
• The sentence is erroneous because the structure of the list is inconsistent. "To ride horses" should be changed to "riding horses" to match "hiking" and "swimming."
• The correct sentence would be: "She enjoys hiking, swimming, and riding horses."
• 3) The presentation was well-received by the audience.
• This sentence describes the positive reception of a presentation.
• This sentence is grammatically and contextually correct.
• 4) Their teamwork and cooperation led to success.
• This sentence discusses the outcome of teamwork and cooperation.
• This sentence is grammatically and contextually correct.
• 5) All are correct.
• This option implies that all the given sentences are correct.
• This option is incorrect because sentence 2 contains an error.

General Solution:

Let:

AC : Number of Cars sold by Company A

AB : Number of Buses sold by Company A

BC : Number of Cars sold by Company B

BB : Number of Buses sold by Company B

CC : Number of Cars sold by Company C

CB : Number of Buses sold by Company C

1. The number of Buses sold by Company C is 20 less than that of Company A:

CB = AB - 20

2. The total number of Buses sold by all three companies is 245:

AB + BB + CB = 245

3. The total number of Buses and Cars sold by Company A is 275:

AC + AB = 275

4. The number of Cars sold by Company C is equal to the number of Cars sold by Company B, which is 120:

CC = BC = 120

5. The ratio of the number of Cars sold by Company A and C is 23:15:

AC / CC = 23 / 15

Since CC = 120:

AC / 120 = 23 / 15

AC = (23 / 15) × 120 = 184

1. From Equation 3:

AC + AB = 275

184 + AB = 275

AB = 91

2. From Equation 1:

CB = AB - 20 = 91 - 20 = 71

3. From Equation 2:

AB + BB + CB = 245

91 + BB + 71 = 245

BB = 245 - 162 = 83

Thus,

 

Calculations:

C_C : Fuel efficiency of Company C's Cars in km/l or any unit.

B_C : Fuel efficiency of Company B's Cars.

A_C : Fuel efficiency of Company A's Cars.

Company B's Cars have a 10% higher fuel efficiency than Company C's Cars:

BC = CC + 0.10 × CC = 1.10 × CC

2. Company A's Cars have a 20% higher fuel efficiency than Company B's Cars:

AC = BC + 0.20 × BC = 1.20 × BC

We know BC = 1.10 × CC. Substitute this into the equation for AC:

AC = 1.20 × BC = 1.20 × 1.10 × CC = 1.32 × CC

So, the fuel efficiency of Company A's Cars is 1.32 × the fuel efficiency of Company C's Cars.

The percentage difference between Company A's Cars and Company C's Cars is:

Percentage Difference = (1.32 - 1) × 100 = 0.32 × 100 = 32%

Thus, the approximate percentage difference in fuel efficiency between Company A's Cars and Company C's Cars is 32%.

General Solution:

Let:

AC : Number of Cars sold by Company A

AB : Number of Buses sold by Company A

BC : Number of Cars sold by Company B

BB : Number of Buses sold by Company B

CC : Number of Cars sold by Company C

CB : Number of Buses sold by Company C

1. The number of Buses sold by Company C is 20 less than that of Company A:

CB = AB - 20

2. The total number of Buses sold by all three companies is 245:

AB + BB + CB = 245

3. The total number of Buses and Cars sold by Company A is 275:

AC + AB = 275

4. The number of Cars sold by Company C is equal to the number of Cars sold by Company B, which is 120:

CC = BC = 120

5. The ratio of the number of Cars sold by Company A and C is 23:15:

AC / CC = 23 / 15

Since CC = 120:

AC / 120 = 23 / 15

AC = (23 / 15) × 120 = 184

1. From Equation 3:

AC + AB = 275

184 + AB = 275

AB = 91

2. From Equation 1:

CB = AB - 20 = 91 - 20 = 71

3. From Equation 2:

AB + BB + CB = 245

91 + BB + 71 = 245

BB = 245 - 162 = 83

Thus,

 

Calculations:

Original price of a Car: Rs. 500,000

Original price of a Bus: Rs. 800,000

Increase in price of a Car by 15%:

New price of a Car = 500,000 + 0.15 × 500,000 = 500,000 + 75,000 = 575,000

Increase in price of a Bus by 10%:

New price of a Bus = 800,000 + 0.10 × 800,000 = 800,000 + 80,000 = 880,000

Original revenue from Cars = 184 × 500,000 = 92,000,000

Original revenue from Buses = 91 × 800,000 = 72,800,000

Total original revenue:

92,000,000 + 72,800,000 = 164,800,000

New revenue from Cars = 184 × 575,000 = 105,800,000

New revenue from Buses = 91 × 880,000 = 80,080,000

Total new revenue:

105,800,000 + 80,080,000 = 185,880,000

Total increase in revenue = New revenue - Original revenue

Total increase in revenue = 185,880,000 - 164,800,000 = 21,080,000

Thus, the total increase in revenue for Company A is Rs. 21,080,000.

General Solution:

Let:

A_C : Number of Cars sold by Company A

A_B : Number of Buses sold by Company A

B_C : Number of Cars sold by Company B

B_B : Number of Buses sold by Company B

C_C : Number of Cars sold by Company C

C_B : Number of Buses sold by Company C

1. The number of Buses sold by Company C is 20 less than that of Company A:

C_B = A_B - 20

2. The total number of Buses sold by all three companies is 245:

A_B + B_B + C_B = 245

3. The total number of Buses and Cars sold by Company A is 275:

A_C + A_B = 275

4. The number of Cars sold by Company C is equal to the number of Cars sold by Company B, which is 120:

C_C = B_C = 120

5. The ratio of the number of Cars sold by Company A and C is 23:15:

A_C / C_C = 23 / 15

Since C_C = 120:

A_C / 120 = 23 / 15

A_C = (23 / 15) × 120 = 184

1. From Equation 3:

A_C + A_B = 275

184 + A_B = 275

A_B = 91

2. From Equation 1:

C_B = A_B - 20 = 91 - 20 = 71

3. From Equation 2:

A_B + B_B + C_B = 245

91 + B_B + 71 = 245

B_B = 245 - 162 = 83

Thus,

 

Calculations:

Total vehicles sold by Company A = 275

Total vehicles sold by Company B = 203

Total vehicles sold by Company C = 191

Total vehicles sold by B and C combined = 203 + 191 = 394

Difference = 394 − 275 = 119.

Thus, the correct answer is 119.

Shortcut Trick

In vessel R, milk is 250% more than water → Milk : Water = 350 : 100 = 7 : 2.

Let 25% of P be 9x → Milk = 5x, Water = 4x. In R: (45 + 5x) / 4x = 7 / 2.

⇒ 90 + 10x = 28x → 18x = 90 → x = 5.

25% of P = 9 × 5 = 45 L → Total P = 180 L. Q = 180 − 20 = 160 L.

Milk in Q = (5/8) × 160 = 100 L.

∴ The correct answer is 100 L.

Alternate Method

Given: Ratio in P = 5:4, Ratio in Q = 5:3, Milk in R = 45 L, Milk = 3.5 × Water in R.

Step 1: Calculate quantities from P to R

⇒ Let 25% of mixture P = 9x. Milk = 5x, Water = 4x.

⇒ In vessel R, Total Milk = 45 + 5x, Total Water = 4x.

⇒ Given: Milk = Water + 250% of Water ⇒ Milk = 3.5 × Water.

⇒ 45 + 5x = 3.5 × 4x ⇒ 45 + 5x = 14x.

⇒ 9x = 45 ⇒ x = 5.

Step 2: Find total quantity of P and Q

⇒ 25% of P = 9 × 5 = 45 L ⇒ Total P = 45 × 4 = 180 L.

⇒ Total Q = Total P − 20 = 180 − 20 = 160 L.

Step 3: Find Milk in Q

⇒ Ratio of Milk : Water in Q = 5 : 3 (Total parts = 8).

⇒ Milk in Q = (5 / 8) × 160 = 100 L.

∴ The correct answer is 100 L.

Additional Information

Mixture Ratio Preservation

When any quantity of a mixture is taken out, the ratio of ingredients in the removed part and the remaining part stays the same as the initial ratio.

Percentage to Ratio Conversion

A value 250% more than x is x + 2.5x = 3.5x. In ratio form, 3.5 : 1 is same as 7 : 2.

Alligation Application

Used to find the mean proportion or the ratio in which two mixtures are mixed. Rule: (Quantity 1 / Quantity 2) = (C₂ − M) / (M − C₁).

Shortcut Trick

Ratio of Marked Price (MP) to Selling Price (SP) for Toy Car based on 15% discount is 100 : 85 or 20 : 17.

Given SP of Toy Car = 850, so 17 units = 850 ⇒ 1 unit = 50.

MP of Toy Car = 20 × 50 = 1000.

From MP:CP ratio (10:9), CP of Toy Car = 900.

Using CP Car : CP Bus (2:1), CP of Toy Bus = 900 ÷ 2 = 450.

Using MP:CP ratio for Bus (11:9), 9 units = 450 ⇒ 11 units = 550.

∴ The correct answer is 550.

Alternate Method

Given: SP_Car = 850, MP_Car:CP_Car = 10:9, MP_Bus:CP_Bus = 11:9, CP_Car:CP_Bus = 2:1, Discount_Car = 15%.

Formulas: SP = MP × (100 − Discount%) ÷ 100 | MP = (SP × 100) ÷ (100 − Discount%).

⇒ MP of Toy Car = (850 × 100) ÷ (100 − 15) = 85000 ÷ 85 = 1000.

⇒ Since MP_Car : CP_Car = 10 : 9, then 10 units = 1000 ⇒ CP of Toy Car = 900.

⇒ Given CP_Car : CP_Bus = 2 : 1, then 2 units = 900 ⇒ CP of Toy Bus = 450.

⇒ Given MP_Bus : CP_Bus = 11 : 9, then 9 units = 450 ⇒ 1 unit = 50.

⇒ MP of Toy Bus = 11 × 50 = 550.

∴ The correct answer is 550.

Additional Information

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). SP = MP − Discount.

Ratio and Proportion in CP/SP

When common terms (like CP) are shared between two ratios, they must be scaled to a common value to compare different articles.

Shortcut Trick

Ratio of Profit = Ratio of (Investment × Time).

Equivalent capital for 1 month for A = (2000 × 4) + (3000 × 4) + (4000 × 4) = 8000 + 12000 + 16000 = 36000.

Equivalent capital for 1 month for B = (3000 × 6) + (4000 × 6) = 18000 + 24000 = 42000.

Profit ratio A : B = 36000 : 42000 = 6 : 7.

Total separated amount = 26000 ⇒ A share + B share = 26000.

Total share of A including charity = A share + x = 15000. Since A share = (6/13) × 26000 = 12000, then x = 15000 − 12000 = 3000.

∴ The correct answer is Rs. 3000.

Alternate Method

Formulas: Profit Ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂) | Total Profit = Amount Separated + Charity (x).

⇒ Total investment of A = (2000 × 4) + (2000+1000) × 4 + (3000+1000) × 4 = 8000 + 12000 + 16000 = Rs. 36,000. ⇒ Total investment of B = (3000 × 6) + (3000+1000) × 6 = 18000 + 24000 = Rs. 42,000. ⇒ Ratio of profits A : B = 36000 : 42000 = 6 : 7. ⇒ Total amount separated = Rs. 26,000. ⇒ Profit share of A = (6 / (6 + 7)) × 26000 = (6 / 13) × 26000 = Rs. 12,000. ⇒ Given: Share given by A including charity (x) = Rs. 15,000. ⇒ x = 15000 − 12000 = Rs. 3,000.

∴ The correct answer is Rs. 3000.

Additional Information

Partnership Rules

In a partnership, profit is distributed based on the product of Capital and Time. If investments change periodically, calculate the weighted sum.

Charity Deduction

If an amount x is deducted for charity from the total profit, the remaining profit is distributed among partners in their investment ratio.

General Solution:

The total employees in a company = Males + Females.

From the given data, we can calculate the total employees for each company using the percentage of female employees.

Formula: Total Employees = Males / (1 - Percentage of Females)

Company A:

Males = 240

Percentage of Females = 40%

Total Employees = 240 / (1 - 0.40) = 240 / 0.60 = 400

Females = 400 - 240 = 160 

Company B:

Males = 275

Percentage of Females = 45%

Total Employees = 275 / (1 - 0.45) = 275 / 0.55 = 500

Females = 500 - 275 = 225 

Company C:

Males = 270

Percentage of Females = 55%

Total Employees =270 / (1 - 0.55) = 270 / 0.45 = 600

Females = 600 - 270 = 330 

Company D:

Males = 120

Percentage of Females = 60%

Total Employees =120 / (1 - 0.60) = 120 / 0.40 = 300

Females = 300 - 120 = 180 

Company E:

Males = 180

Percentage of Females = 50%

Total Employees =180 / (1 - 0.50) = 180 / 0.50 = 360

Females = 360 - 180 = 180 

Calculations:

Average employees in D and F = 275

Total employees in D and F = 275 × 2 = 550

From Step 1, total employees in D = 300

So, total employees in F = 550 - 300 = 250 

Total female employees in D and F = 270

From Step 1, female employees in D = 180

So, female employees in F = 270 - 180 = 90 

Total employees in F = 250

Female employees in F = 90

Male employees in F = 250 - 90 = 160 

Male employees in C = 270

Male employees in F = 160

Difference = 270 -160 = 110

Percentage difference = 110 / 160 × 100 = 68.75% 

Thus, the Male employees in C are 68.75% more than male employees in F.

General Solution:

The total employees in a company = Males + Females.

From the given data, we can calculate the total employees for each company using the percentage of female employees.

Formula: Total Employees = Males / (1 - Percentage of Females)

Company A:

Males = 240

Percentage of Females = 40%

Total Employees = 240 / (1 - 0.40) = 240 / 0.60 = 400

Females = 400 - 240 = 160 

Company B:

Males = 275

Percentage of Females = 45%

Total Employees = 275 / (1 - 0.45) = 275 / 0.55 = 500

Females = 500 - 275 = 225 

Company C:

Males = 270

Percentage of Females = 55%

Total Employees =270 / (1 - 0.55) = 270 / 0.45 = 600

Females = 600 - 270 = 330 

Company D:

Males = 120

Percentage of Females = 60%

Total Employees =120 / (1 - 0.60) = 120 / 0.40 = 300

Females = 300 - 120 = 180 

Company E:

Males = 180

Percentage of Females = 50%

Total Employees =180 / (1 - 0.50) = 180 / 0.50 = 360

Females = 360 - 180 = 180 

Calculations:

Male Employees in A and B Together:

240 (A) + 275 (B) = 515

Female Employees in D and E Together:

180 (D) + 180 (E) = 360

Difference:

515 - 360 = 155

Thus, the difference is 155.

General Solution:

The total employees in a company = Males + Females.

From the given data, we can calculate the total employees for each company using the percentage of female employees.

Formula: Total Employees = Males / (1 - Percentage of Females)

Company A:

Males = 240

Percentage of Females = 40%

Total Employees = 240 / (1 - 0.40) = 240 / 0.60 = 400

Females = 400 - 240 = 160 

Company B:

Males = 275

Percentage of Females = 45%

Total Employees = 275 / (1 - 0.45) = 275 / 0.55 = 500

Females = 500 - 275 = 225 

Company C:

Males = 270

Percentage of Females = 55%

Total Employees =270 / (1 - 0.55) = 270 / 0.45 = 600

Females = 600 - 270 = 330 

Company D:

Males = 120

Percentage of Females = 60%

Total Employees =120 / (1 - 0.60) = 120 / 0.40 = 300

Females = 300 - 120 = 180 

Company E:

Males = 180

Percentage of Females = 50%

Total Employees =180 / (1 - 0.50) = 180 / 0.50 = 360

Females = 360 - 180 = 180 

Calculations:

60% of total employees in Company A are aged above 40 years.

Number of employees aged above 40 = 60% × 400 = 240 

Half of the employees aged above 40 are females.

Number of females aged above 40 = 240 / 2 = 120 

Total employees aged above 40 = 240

Females aged above 40 = 120

Males aged above 40 = 240 - 120 = 120 

Or

Males aged ≤ 40 = 240 - 120 = 120

Thus, the number of males aged ≤ 40 years in Company A is 120.

General Solution:

The total employees in a company = Males + Females.

From the given data, we can calculate the total employees for each company using the percentage of female employees.

Formula: Total Employees = Males / (1 - Percentage of Females)

Company A:

Males = 240

Percentage of Females = 40%

Total Employees = 240 / (1 - 0.40) = 240 / 0.60 = 400

Females = 400 - 240 = 160 

Company B:

Males = 275

Percentage of Females = 45%

Total Employees = 275 / (1 - 0.45) = 275 / 0.55 = 500

Females = 500 - 275 = 225 

Company C:

Males = 270

Percentage of Females = 55%

Total Employees =270 / (1 - 0.55) = 270 / 0.45 = 600

Females = 600 - 270 = 330 

Company D:

Males = 120

Percentage of Females = 60%

Total Employees =120 / (1 - 0.60) = 120 / 0.40 = 300

Females = 300 - 120 = 180 

Company E:

Males = 180

Percentage of Females = 50%

Total Employees =180 / (1 - 0.50) = 180 / 0.50 = 360

Females = 360 - 180 = 180 

Calculations:

Let's calculate the number of employees receiving benefits:

Company C (Promotions):

Male employees in C: 270

Promoted males: 30% of 270 = 0.30 × 270 = 81

Company A (Responsibilities):

Female employees in A: 160

Females with responsibilities: 35% of 160 = 0.35 × 160 = 56

Company E (Bonuses):

Total employees in E: 360

Employees with bonuses: 40% of 360 = 0.40 × 360 = 144

Now, let's calculate the number of employees NOT receiving benefits:

Company C:

Total employees in C: 600

Employees without promotions: 600 - 81 = 519

Company A:

Total employees in A: 400

Employees without responsibilities: 400 - 56 = 344

Company E:

Total employees in E: 360

Employees without bonuses: 360 - 144 = 216

So,

Total employees without benefits: 519 (C) + 344 (A) + 216 (E) = 1079

Therefore, the total number of employees in these three companies who did not receive any promotion, responsibility, or bonus is 1079.

General Solution:

The total employees in a company = Males + Females.

From the given data, we can calculate the total employees for each company using the percentage of female employees.

Formula: Total Employees = Males / (1 - Percentage of Females)

Company A:

Males = 240

Percentage of Females = 40%

Total Employees = 240 / (1 - 0.40) = 240 / 0.60 = 400

Females = 400 - 240 = 160 

Company B:

Males = 275

Percentage of Females = 45%

Total Employees = 275 / (1 - 0.45) = 275 / 0.55 = 500

Females = 500 - 275 = 225 

Company C:

Males = 270

Percentage of Females = 55%

Total Employees =270 / (1 - 0.55) = 270 / 0.45 = 600

Females = 600 - 270 = 330 

Company D:

Males = 120

Percentage of Females = 60%

Total Employees =120 / (1 - 0.60) = 120 / 0.40 = 300

Females = 300 - 120 = 180 

Company E:

Males = 180

Percentage of Females = 50%

Total Employees =180 / (1 - 0.50) = 180 / 0.50 = 360

Females = 360 - 180 = 180 

Calculations:

Company A:

Original males = 240

Increase by 25% = 240 × 1.25 = 300

Company B:

Original males = 275

Decrease by 20% = 275 × 0.80 = 220

Company C:

Original males = 270

Increase by 10% = 270 × 1.10 = 297

Company A:

Percentage of females = 40%

Total employees = 300 / (1 - 0.40) = 300 / 0.60 = 500

Company B:

Percentage of females = 45%

Total employees = 220 / (1 - 0.45) = 220 / 0.55 = 400

Company C:

Percentage of females = 55%

Total employees = 297 / (1 - 0.55) = 297 / 0.45 = 660

Total employees in A : B : C = 500 : 400 : 660 = 25 : 20 : 33

Thus, the new ratio is 25:20:33.

Shortcut Trick

Ratio of Profit share = (Investment_A × Time_A) : (Investment_B × Time_B) : (Investment_C × Time_C).

From A and B's profit ratio: (4500 × y) : (5500 × (y + 3)) = 63 : 110.

9y : 11(y + 3) = 63 : 110 ⇒ 9y ÷ (11y + 33) = 63 ÷ 110 ⇒ y ÷ (y + 3) = 7 ÷ 10.

10y = 7y + 21 ⇒ 3y = 21 ⇒ y = 7.

Total Profit = 79250, Charity = 20%, Remaining = 80% of 79250 = 63400.

Profit share of A = [63 ÷ (63 + 110 + 144)] × 63400 = (63 ÷ 317) × 63400 = 12600. Required ratio = 12600 ÷ 7 = 1800.

∴ The correct answer is 1800.

Alternate Method

Given → Investments: A = 4500, B = 5500, C = 6000. Time: A = y, B = y + 3, C = 12. Profit Ratio = 63 : 110 : 144. Total Profit = 79250. Formulas: Profit Share = Investment × Time | Remaining Profit = Total × (100 − Charity%) ÷ 100.

⇒ Calculate y using A and C: (4500 × y) ÷ (6000 × 12) = 63 ÷ 144. ⇒ 4500y ÷ 72000 = 63 ÷ 144 ⇒ y ÷ 16 = 63 ÷ 144 ⇒ y = (63 × 16) ÷ 144 = 7. ⇒ Net Profit after charity = 79250 × 0.8 = 63400. ⇒ Profit of A = [63 ÷ (63 + 110 + 144)] × 63400 = (63 ÷ 317) × 63400 = 63 × 200 = 12600. ⇒ Required value = Profit of A ÷ y = 12600 ÷ 7 = 1800.

∴ The correct answer is 1800.

Additional Information

Partnership Basics

In a partnership, profits are distributed in the ratio of the product of Investment and Time period. Profit Share = Capital × Time.

Effective Profit

When a portion of profit is donated to charity or kept as a reserve, the remaining profit is distributed among partners based on their investment-time ratios.

Shortcut Trick

Interest from Scheme P = 1500 × 11.25% × 4 = 1500 × 45% = ₹675.

Interest from Scheme Q = 1200 × 25% × X = 300X.

Equating both: 300X = 675 ⇒ X = 2.25 years.

Rate for Scheme R = 4X% = 4 × 2.25 = 9%.

Interest from Scheme R = 2000 × 9% × 2 = ₹360.

∴ The correct answer is 360 Rs.

Alternate Method

Given: Principal P₁ = ₹1500, R₁ = 11.25%, T₁ = 4 years; Principal P₂ = ₹1200, R₂ = 25%, T₂ = X years; Principal P₃ = ₹2000, R₃ = 4X%, T₃ = 2 years.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100

⇒ SI_P = (1500 × 11.25 × 4) ÷ 100 = 15 × 45 = ₹675

⇒ SI_Q = (1200 × 25 × X) ÷ 100 = 12 × 25 × X = 300X

⇒ Since SI_P = SI_Q, 300X = 675 ⇒ X = 675 ÷ 300 = 2.25

⇒ For Scheme R: Rate = 4X% = 4 × 2.25 = 9%

⇒ Interest in Scheme R = (2000 × 9 × 2) ÷ 100 = 20 × 18 = ₹360

∴ The correct answer is 360 Rs.

Additional Information

Simple Interest Property

Simple Interest is calculated only on the Principal amount. It remains constant for every year if the rate and principal are unchanged.

Effective Rate of Interest

The total interest percentage over a period is the product of Rate (R) and Time (T). Total Interest = (R × T)% of Principal.

Comparison of Interests

When interests are equal, P₁R₁T₁ = P₂R₂T₂. This relation can be used to find any missing variable directly.

Shortcut Trick

Let Upstream speed be U and Downstream speed be D.

Given U + D = 30. Using trial values from the sum: If U = 9 and D = 21 (since 9+21=30):

Case 1: 72/9 + 180/21 = 8 + 8.57 ≠ 16. If U = 12 and D = 18: 72/12 + 180/18 = 6 + 10 = 16 hours (Satisfied).

Case 2: 108/12 + 126/18 = 9 + 7 = 16 hours (Satisfied). U = 12 kmph, D = 18 kmph.

Speed of stream = (D − U) ÷ 2 = (18 − 12) ÷ 2 = 3 kmph.

∴ The correct answer is 3 kmph.

Alternate Method

Given:

Distance Upstream₁ = 72 km, Distance Downstream₁ = 180 km, Time₁ = 16 hours

Distance Upstream₂ = 108 km, Distance Downstream₂ = 126 km, Time₂ = 16 hours

Formula Used: Time = Distance ÷ Speed; Stream Speed = (D − U) ÷ 2

⇒ 72/U + 180/D = 16 ---- (i)

⇒ 108/U + 126/D = 16 ---- (ii)

⇒ Since both equal 16: 72/U + 180/D = 108/U + 126/D

⇒ 180/D − 126/D = 108/U − 72/U

⇒ 54/D = 36/U ⇒ D/U = 54/36 = 3/2

⇒ Let D = 3k and U = 2k. Given U + D = 30 ⇒ 5k = 30 ⇒ k = 6

⇒ D = 18 kmph, U = 12 kmph

⇒ Speed of stream = (18 − 12) ÷ 2 = 6 ÷ 2 = 3 kmph

∴ The correct answer is 3 kmph.

Additional Information

Boat Speed in Still Water

It is the average of downstream and upstream speeds: B = (D + U) ÷ 2.

Speed of Stream

It is half the difference between downstream and upstream speeds: S = (D − U) ÷ 2.

Relative Speed in Water

Downstream Speed (D) = Speed of Boat (B) + Speed of Stream (S); Upstream Speed (U) = B − S.

Shortcut Trick

Let Q's present age be 11x and R's present age be 15x.

From (P − 5) : (11x + 5) = 2 : 3 ⇒ P = (22x + 10)/3 + 5.

Using P + R = 120 ⇒ (22x + 25)/3 + 15x = 120 ⇒ 67x = 335 ⇒ x = 5.

P = 45 years, Q = 55 years. Since (P + y) : (Q + 5) = 1 : 1 ⇒ 45 + y = 60.

∴ The correct answer is 15 years.

Alternate Method

Given: Ratio (P − 5) : (Q + 5) = 2 : 3, Q : R = 11 : 15, P + R = 120.

⇒ Let Q = 11x and R = 15x.

⇒ (P − 5) / (11x + 5) = 2 / 3

⇒ 3P − 15 = 22x + 10 ⇒ 3P − 22x = 25 --- (Eq. 1)

⇒ P + 15x = 120 ⇒ P = 120 − 15x --- (Eq. 2)

⇒ Substitute Eq. 2 in Eq. 1: 3(120 − 15x) − 22x = 25

⇒ 360 − 45x − 22x = 25 ⇒ 335 = 67x ⇒ x = 5.

⇒ Present Age of Q = 11 × 5 = 55 years.

⇒ Present Age of P = 120 − 15(5) = 45 years.

⇒ (P + y) / (Q + 5) = 1 / 1 ⇒ 45 + y = 55 + 5

⇒ 45 + y = 60 ⇒ y = 15.

∴ The correct answer is 15.

Additional Information

Ratio of Ages

If the ratio of ages is a:b, we assume ages as ax and bx. The difference between ages remains constant over time.

Linear Equations in Ages

Age n years ago = (Present Age − n). Age n years hence = (Present Age + n).

Proportion Rule

If two quantities are in ratio 1:1, it implies they are equal to each other.

Considering the given series

9, 10, 22, 70, 280, 1405

The logic of the given series can be explained as

9 × 1 + 1 = 10

10 × 2 + 2 = 22

22 × 3 + 3 = 69

69 × 4 + 4= 280

280 × 5 + 5 = 1405

∴ Wrong term in given number series is 70.

GIVEN:

144, 2197, 196, 3375, 256, 4903

CALCULATION:

⇒ 17³ = 4913

⇒ So, 4903 is the wrong term.

Considering the given series

49, 110, 174, 244, 323, 412, 520

The logic of the given series can be explained as

 

∴ Wrong term in given number series is 412.

Shortcut Trick

Initial Savings: A = ₹9000 (75% of x), B = ₹10000 (66.67% of y).

New Savings: Since expenditure percentage remains same, savings percentage also remains same.

New Savings of A = 9000 × 1.5 = ₹13500 | New Savings of B = 10000 × 1.4 = ₹14000.

Difference = 14000 − 13500 = ₹500.

∴ The correct answer is Rs. 500.

Alternate Method

Given:

Savings of A = 75% of x = ₹9000 ⇒ x = 9000 ÷ 0.75 = ₹12000

Savings of B = 66.67% of y = ₹10000 ⇒ y = 10000 ÷ (2/3) = ₹15000

New Calculations:

⇒ New Income A = 12000 × 150% = ₹18000

⇒ New Expenditure A = 25% of 18000 = ₹4500

⇒ New Savings A = 18000 − 4500 = ₹13500

⇒ New Income B = 15000 × 140% = ₹21000

⇒ New Expenditure B = 33.333% of 21000 = 1/3 × 21000 = ₹7000

⇒ New Savings B = 21000 − 7000 = ₹14000

⇒ Difference = 14000 − 13500 = ₹500

∴ The correct answer is Rs. 500.

Additional Information

Income, Expenditure and Savings Relationship

The basic formula is Income = Expenditure + Savings. If the expenditure percentage remains constant, savings will grow at the same rate as income.

Percentage to Fraction Conversion

Useful conversions: 25% = 1/4, 75% = 3/4, 33.333% = 1/3, and 66.666% = 2/3.

Shortcut Trick

Total Work (LCM of 8, 12, 6) = 24 units.

Efficiencies: A = 3, B = 2, C = 4. Combined B+C = 6.

Work Equation: (B+C)×x + A×(x+2) = 24 ⇒ 6x + 3(x+2) = 24 ⇒ 9x = 18 ⇒ x = 2.

Work by A in (x+4) = 6 days: 3 × 6 = 18 units.

Percentage = (18/24) × 100 = 75%.

∴ The correct answer is 75%.

Alternate Method

Given: Time taken by A = 8 days, B = 12 days, C = 6 days.

Formula Used: Total Work = Efficiency × Time; Efficiency = Total Work ÷ Time.

Calculations:

⇒ Work done by B and C in x days = (2 + 4) × x = 6x units.

⇒ Work done by A in (x + 2) days = 3 × (x + 2) = 3x + 6 units.

⇒ Total Work: 6x + 3x + 6 = 24

⇒ 9x = 18 ⇒ x = 2.

⇒ If A alone works for (x + 4) days = (2 + 4) = 6 days.

⇒ Work done by A in 6 days = 3 × 6 = 18 units.

⇒ Percentage of work completed = (18 ÷ 24) × 100

⇒ Percentage = 0.75 × 100 = 75%.

∴ The correct answer is 75%.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete the work (E ∝ 1/T).

Remaining Work Calculation

Remaining Work = Total Work − Work already completed by previous group of workers.

Combined Efficiency

When people work together, their individual efficiencies are added to find the total rate of work (E_Total = E₁ + E₂ + ...).

General Solution:

Determine the value of 'x':

The sum of the percentages of profit from all items must equal 100%.

Therefore: (2x - 2) + (x + 1) + (x + 3) + (x - 1) + (x + 9) = 100

6x + 10 = 100

6x = 90

x = 15

Now, let's calculate the percentage of profit earned from each item:

Bag: (2 × 15 - 2)% = 28%

Bottle: (15 + 1)% = 16%

Box: (15 + 3)% = 18%

Pen: (15 - 1)% = 14%

Register: (15 + 9)% = 24%

Now, let's calculate the actual profit (in Rupees) earned from each item:

Bag: 28% of Rs. 25,000 = 0.28 × 25,000 = Rs. 7,000

Bottle: 16% of Rs. 25,000 = 0.16 × 25,000 = Rs. 4,000

Box: 18% of Rs. 25,000 = 0.18 × 25,000 = Rs. 4,500

Pen: 14% of Rs. 25,000 = 0.14 × 25,000 = Rs. 3,500

Register: 24% of Rs. 25,000 = 0.24 × 25,000 = Rs. 6,000

Calculations:

Profit from bags = Rs. 7,000

Percentage reinvested = 45%

Amount reinvested = (45/100) × 7,000 = Rs. 3,150

Profit from registers = Rs. 6,000

Percentage reinvested = 60%

Amount reinvested = (60/100) × 6,000 = Rs. 3,600

Total reinvested = 3,150 + 3,600 = Rs. 6,750

Thus, the correct answer is Rs. 6,750

General Solution:

Determine the value of 'x':

The sum of the percentages of profit from all items must equal 100%.

Therefore: (2x - 2) + (x + 1) + (x + 3) + (x - 1) + (x + 9) = 100

6x + 10 = 100

6x = 90

x = 15

Now, let's calculate the percentage of profit earned from each item:

Bag: (2 × 15 - 2)% = 28%

Bottle: (15 + 1)% = 16%

Box: (15 + 3)% = 18%

Pen: (15 - 1)% = 14%

Register: (15 + 9)% = 24%

Now, let's calculate the actual profit (in Rupees) earned from each item:

Bag: 28% of Rs. 25,000 = 0.28 × 25,000 = Rs. 7,000

Bottle: 16% of Rs. 25,000 = 0.16 × 25,000 = Rs. 4,000

Box: 18% of Rs. 25,000 = 0.18 × 25,000 = Rs. 4,500

Pen: 14% of Rs. 25,000 = 0.14 × 25,000 = Rs. 3,500

Register: 24% of Rs. 25,000 = 0.24 × 25,000 = Rs. 6,000

Calculations:

We are given:

The cost price CP of all registers = ₹19,000

Profit earned on registers = ₹6,000

The total selling price SP of all registers = CP + Profit = ₹19,000 + ₹6,000 = ₹25,000

The marked price MP of all registers is 40% above the cost price

Since the marked price is 40% more than the cost price, we calculate:

MP = CP + 40% of CP

MP = 19000 + (40 / 100 × 19000)

MP = 19000 + 7600 = 26600

The discount is given on the marked price to reach the selling price.

So, the discount amount is:

Discount = MP − SP = 26600 − 25000 = 1600

Now, the discount percentage is:

Discount % = Discount / Marked Price × 100 = 1600 / 26600 × 100 ≈ 6.02%

Thus, the approximate percentage discount applied to the marked price is 6%.

General Solution:

Determine the value of 'x':

The sum of the percentages of profit from all items must equal 100%.

Therefore: (2x - 2) + (x + 1) + (x + 3) + (x - 1) + (x + 9) = 100

6x + 10 = 100

6x = 90

x = 15

Now, let's calculate the percentage of profit earned from each item:

Bag: (2 × 15 - 2)% = 28%

Bottle: (15 + 1)% = 16%

Box: (15 + 3)% = 18%

Pen: (15 - 1)% = 14%

Register: (15 + 9)% = 24%

Now, let's calculate the actual profit (in Rupees) earned from each item:

Bag: 28% of Rs. 25,000 = 0.28 × 25,000 = Rs. 7,000

Bottle: 16% of Rs. 25,000 = 0.16 × 25,000 = Rs. 4,000

Box: 18% of Rs. 25,000 = 0.18 × 25,000 = Rs. 4,500

Pen: 14% of Rs. 25,000 = 0.14 × 25,000 = Rs. 3,500

Register: 24% of Rs. 25,000 = 0.24 × 25,000 = Rs. 6,000

Calculations:

Given that the profit percentage for the Notebook is:

(0.5x + 5)%

Substituting x = 15 from the general solution:

0.5 × 15 + 5 = 7.5 + 5 = 12.5%

Thus, the Notebook represents 12.5% of the total profit.

Now, the total profit percentage must still sum to 100%, but we have added the Notebook while keeping the total profit constant.

The original sum of the profit percentages was 100% from 5 items. Now, the Notebook takes 12.5%, meaning the remaining 87.5% must be redistributed among the previous five items in the same proportion.

The adjusted percentage for each previous item is calculated as:

New Percentage = Old Percentage / 100 × 87.5

Bag: 28 / 100 × 87.5 = 24.5%

Bottle: 16 / 100 × 87.5 = 14%

Box: 18 / 100 × 87.5 = 15.75%

Pen: 14 / 100 × 87.5 = 12.25%

Register: 24 / 100 × 87.5 = 21%

Thus, the new percentage of profit from the Pen is 12.25%.

Thus,

Notebook represents 12.5% of the total profit.

New profit percentage of the Pen: 12.25%.

General Solution:

Determine the value of 'x':

The sum of the percentages of profit from all items must equal 100%.

Therefore: (2x - 2) + (x + 1) + (x + 3) + (x - 1) + (x + 9) = 100

6x + 10 = 100

6x = 90

x = 15

Now, let's calculate the percentage of profit earned from each item:

Bag: (2 × 15 - 2)% = 28%

Bottle: (15 + 1)% = 16%

Box: (15 + 3)% = 18%

Pen: (15 - 1)% = 14%

Register: (15 + 9)% = 24%

Now, let's calculate the actual profit (in Rupees) earned from each item:

Bag: 28% of Rs. 25,000 = 0.28 × 25,000 = Rs. 7,000

Bottle: 16% of Rs. 25,000 = 0.16 × 25,000 = Rs. 4,000

Box: 18% of Rs. 25,000 = 0.18 × 25,000 = Rs. 4,500

Pen: 14% of Rs. 25,000 = 0.14 × 25,000 = Rs. 3,500

Register: 24% of Rs. 25,000 = 0.24 × 25,000 = Rs. 6,000

Calculations:

Profit from pens = Rs. 3,500

15% donation from pens = 15 / 100 × 3,500 = 525

Profit from bottles = Rs. 4,000

20% donation from bottles = 20 / 100 × 4,000 = 800

Remaining profit after donation = 3,500 − 525 = 2,975

30% of remaining profit from pens = 30 / 100 × 2,975 = 892.5

Final remaining profit = 2,975 − 892.5 = 2,082.5

Thus, the correct answer is ₹2,082.50

General Solution:

Determine the value of 'x':

The sum of the percentages of profit from all items must equal 100%.

Therefore: (2x - 2) + (x + 1) + (x + 3) + (x - 1) + (x + 9) = 100

6x + 10 = 100

6x = 90

x = 15

Now, let's calculate the percentage of profit earned from each item:

Bag: (2 × 15 - 2)% = 28%

Bottle: (15 + 1)% = 16%

Box: (15 + 3)% = 18%

Pen: (15 - 1)% = 14%

Register: (15 + 9)% = 24%

Now, let's calculate the actual profit (in Rupees) earned from each item:

Bag: 28% of Rs. 25,000 = 0.28 × 25,000 = Rs. 7,000

Bottle: 16% of Rs. 25,000 = 0.16 × 25,000 = Rs. 4,000

Box: 18% of Rs. 25,000 = 0.18 × 25,000 = Rs. 4,500

Pen: 14% of Rs. 25,000 = 0.14 × 25,000 = Rs. 3,500

Register: 24% of Rs. 25,000 = 0.24 × 25,000 = Rs. 6,000

Calculations:

From the general solution:

Profit on Box = Rs. 4,500

Profit on Pen = Rs. 3,500

Selling Price of Box:

Cost Price (CP) of Box = Rs. 15,000

Profit = Rs. 4,500

Selling Price (SP) of Box = CP + Profit = 15,000 + 4,500 = Rs. 19,500

Selling Price of Pen:

Cost Price CP of Pen = Rs. 20,000

Profit = Rs. 3,500

Selling Price (SP) of Pen = CP + Profit = 20,000 + 3,500 = Rs. 23,500

Box: Selling price increases by 20%

New SP of Box = 19,500 × 1.20 = Rs. 23,400

Pen: Selling price decreases by 10%

New SP of Pen = 23,500 × 0.90 = Rs. 21,150

New Profit on Box:

New SP of Box = Rs. 23,400

CP of Box = Rs. 15,000

New Profit = 23,400 15,000 = Rs. 8,400

New Profit on Pen:

New SP of Pen = Rs. 21,150

CP of Pen = Rs. 20,000

New Profit = 21,150 - 20,000 = Rs. 1,150

From the general solution, the original profits on other items are:

Bag = Rs. 7,000

Bottle = Rs. 4,000

Register = Rs. 6,000

New profits:

Box = Rs. 8,400

Pen = Rs. 1,150

Total new profit = 7,000 + 4,000 + 8,400 + 1,150 + 6,000 = Rs. 26,550

Thus, the new total profit earned by the shopkeeper is Rs. 26,550.

General Solution:

Determine the value of 'x':

The sum of the percentages of profit from all items must equal 100%.

Therefore: (2x - 2) + (x + 1) + (x + 3) + (x - 1) + (x + 9) = 100

6x + 10 = 100

6x = 90

x = 15

Now, let's calculate the percentage of profit earned from each item:

Bag: (2 × 15 - 2)% = 28%

Bottle: (15 + 1)% = 16%

Box: (15 + 3)% = 18%

Pen: (15 - 1)% = 14%

Register: (15 + 9)% = 24%

Now, let's calculate the actual profit (in Rupees) earned from each item:

Bag: 28% of Rs. 25,000 = 0.28 × 25,000 = Rs. 7,000

Bottle: 16% of Rs. 25,000 = 0.16 × 25,000 = Rs. 4,000

Box: 18% of Rs. 25,000 = 0.18 × 25,000 = Rs. 4,500

Pen: 14% of Rs. 25,000 = 0.14 × 25,000 = Rs. 3,500

Register: 24% of Rs. 25,000 = 0.24 × 25,000 = Rs. 6,000

Calculations:

We are given:

Total bottles sold = 500

Cost price per bottle = Rs. 50

Originally, all bottles were sold at a 20% profit.

Selling price per bottle = Cost price + 20% profit = 50 + 20 / 100 × 50 = 50 + 10 = 60 

20% of bottles are defective

20 / 100 × 500 = 100 defective bottles

These defective bottles were sold at a 15% loss.

Selling price per defective bottle = Cost price − 15% loss = 50 − 15 / 100 × 50 = 50 − 7.5 = 42.5

Total loss from defective bottles:

Total loss = 50 − 42.5 × 100 = 7.5 × 100 = 750 

We initially had a profit of Rs. 4,000 from bottles.

Net profit = Initial profit − Loss from defective bottles = 4,000 − 750 = 3,250

Thus, the net profit earned from bottles after accounting for defective items is Rs. 3,250.

Shortcut Trick

Let speed of Car A be S_A and Car B be S_B.

From the second condition: Total Distance = (Relative Speed) × Time

⇒ 160 = [S_A + (S_B + 10)] × 2 ⇒ S_A + S_B = 70 kmph.

Using the first condition (distance 120 km, 1 hr difference): Try values that sum to 70.

If S_A = 30 and S_B = 40: (120/30) − (120/40) = 4 − 3 = 1 hour. This satisfies all conditions.

∴ The correct answer is 30 kmph.

Alternate Method

Given: Distance = 120 km, Time difference = 1 hr, Distance apart = 160 km, Meeting time = 2 hr.

Case 1: Movement in opposite directions

⇒ Relative Speed = S_A + (S_B + 10)

⇒ 160 / 2 = S_A + S_B + 10

⇒ 80 = S_A + S_B + 10 ⇒ S_A + S_B = 70 --- (i)

Case 2: Time difference for 120 km

⇒ (120 / S_A) − (120 / S_B) = 1

⇒ 120 × (S_B − S_A) = S_A × S_B

Substitute S_B = 70 − S_A from (i):

⇒ 120 × (70 − S_A − S_A) = S_A(70 − S_A)

⇒ 120(70 − 2S_A) = 70S_A − S_A²

⇒ 8400 − 240S_A = 70S_A − S_A²

⇒ S_A² − 310S_A + 8400 = 0

⇒ (S_A − 30)(S_A − 280) = 0

⇒ Since speed < 100 kmph, S_A = 30 kmph.

∴ The correct answer is 30 kmph.

Additional Information

Relative Speed

When two objects move in opposite directions, relative speed is the sum of their individual speeds (u + v). When moving in the same direction, it is the difference (u − v).

Time, Speed, and Distance Relation

For a constant distance, time is inversely proportional to speed. T₁/T₂ = S₂/S₁.

Meeting Time Formula

Meeting Time = (Initial distance between objects) ÷ (Relative Speed).

Shortcut Trick

Let n be the number of students and A be the original average.

Case 1: 30 − A = 2(n + 1) ⇒ 30 − A = 2n + 2 ⇒ 2n + A = 28

Case 2: 54 − 2A = 3(n + 2) ⇒ 54 − 2A = 3n + 6 ⇒ 3n + 2A = 48

Multiply Case 1 by 2: 4n + 2A = 56. Subtract Case 2: (4n − 3n) = 56 − 48 ⇒ n = 8.

Substitute n = 8 in Case 1: 2(8) + A = 28 ⇒ 16 + A = 28 ⇒ A = 12 kg.

∴ The correct answer is 12 kg.

Alternate Method

Given: Original average = A, Total students = n.

Formula: Total Weight = Average × Number of students.

⇒ Case 1: (nA + 30) = (n + 1)(A + 2)

⇒ nA + 30 = nA + 2n + A + 2 ⇒ 2n + A = 28 ... (i)

⇒ Case 2: (nA + 2 × 27) = (n + 2)(A + 3)

⇒ nA + 54 = nA + 3n + 2A + 6 ⇒ 3n + 2A = 48 ... (ii)

⇒ From (i), A = 28 − 2n. Substitute in (ii):

⇒ 3n + 2(28 − 2n) = 48 ⇒ 3n + 56 − 4n = 48

⇒ −n = −8 ⇒ n = 8 students

⇒ A = 28 − 2(8) = 28 − 16 = 12 kg

∴ The correct answer is 12 kg.

Additional Information

Net Deviation Method

In average problems, the sum of deviations from the original average is equal to the total increase or decrease in weight across all members (Net Deviation = Change in Average × New Total Count).

Weighted Average

When two groups are combined, the new average A_w = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick Using Total Surface Area (TSA) formula: 2πr(r + h) = 960 with π = 3. ⇒ 2 × 3 × (x − 4)(x − 4 + x) = 960 ⇒ (x − 4)(2x − 4) = 160. ⇒ (x − 4)(x − 2) = 80. By inspection, if x = 12, then 8 × 10 = 80. Breadth (b) = x = 12 cm. CSA = 2 × 3 × 8 × 12 = 576 cm2. Perimeter (P) = 576 − 492 = 84 cm. 2(L + 12) = 84 ⇒ L = 30 cm. Area = 30 × 12 = 360 cm2. ∴ The correct answer is 360 cm2. Alternate Method Given: TSA = 960 cm2, π = 3, Height (h) = x, Radius (r) = x − 4, Breadth (b) = x. Formula Used: TSA = 2πr(h + r); CSA = 2πrh; Perimeter = 2(L + b); Area = L × b.

⇒ 2 × 3 × (x − 4)(x + x − 4) = 960 ⇒ 6 × (x − 4)(2x − 4) = 960 ⇒ (x − 4) × 2(x − 2) = 160 ⇒ x2 − 6x + 8 = 80 ⇒ x2 − 6x − 72 = 0 ⇒ (x − 12)(x + 6) = 0 ⇒ x = 12 cm (as x > 0) ⇒ Radius (r) = 12 − 4 = 8 cm; Height (h) = 12 cm; Breadth (b) = 12 cm ⇒ CSA of Cylinder = 2 × 3 × 8 × 12 = 576 cm2 ⇒ Perimeter of Rectangle = CSA − 492 = 576 − 492 = 84 cm ⇒ 2(L + 12) = 84 ⇒ L + 12 = 42 ⇒ L = 30 cm ⇒ Area of Rectangle = 30 × 12 = 360 cm2 ∴ The correct answer is 360 cm2. Additional Information Cylinder Formulas Curved Surface Area = 2πrh. Total Surface Area = 2πr(h + r). Volume = πr2h. Rectangle Properties Perimeter = 2(Length + Breadth). Area = Length × Breadth. Diagonal = √(L2 + B2). Quadratic Roots Shortcut For ax2 + bx + c = 0, find two numbers that multiply to ac and add to b, then change signs and divide by a.

Shortcut Trick

Equate the sum of individual honey parts to the total honey in the final mixture.

Total Honey = (7/10)×(x+20) + (3/5)×(x−30) + (5/8)×(2x)

Total Water = (3/10)×(x+20) + (2/5)×(x−30) + (3/8)×(2x)

Ratio 20:11 ⇒ 11×Honey = 20×Water. Solving gives x = 80.

Calculate 2.5x = 2.5 × 80 = 200 ml.

∴ The correct answer is 200 ml.

Alternate Method

Given: Ratio of Honey : Water in Y = 7:3, Z = 3:2, T = 5:3. Final Ratio = 20:11.

⇒ Honey from Y = 0.7(x + 20) = 0.7x + 14

⇒ Honey from Z = 0.6(x − 30) = 0.6x − 18

⇒ Honey from T = (5/8) × 2x = 1.25x

⇒ Total Honey = 0.7x + 14 + 0.6x − 18 + 1.25x = 2.55x − 4

⇒ Total Mixture = (x + 20) + (x − 30) + 2x = 4x − 10

⇒ (Total Honey) / (Total Mixture) = 20 / (20 + 11) = 20/31

⇒ (2.55x − 4) / (4x − 10) = 20 / 31

⇒ 31(2.55x − 4) = 20(4x − 10)

⇒ 79.05x − 124 = 80x − 200

⇒ 0.95x = 76 ⇒ x = 76 / 0.95 = 80

⇒ 2.5x = 2.5 × 80 = 200

∴ The correct answer is 200 ml.

Additional Information

Mixture Rule

When multiple mixtures are combined, the total quantity of a specific component is the sum of that component in each individual mixture.

Ratio to Fraction

If the ratio of A:B is m:n, then the quantity of A in a total volume V is [m/(m+n)] × V.

Weighted Average of Ratios

Final concentration C = (q₁c₁ + q₂c₂ + ... + q_nc_n) / (q₁ + q₂ + ... + q_n).

1. X born in a month which have odd number of days but not on even date of a month.

2. Only one person born between X and O.

3. More than three person born between E and the person who lives in Delhi.

 

4. J lives in a city which start with the same alphabetical letter. Therefore, case 1 further divided into two cases.

5. Person who lives in Mumbai born immediately after O.

 

6. Only three person born between R and the person who lives in Patna. Therefore, case 1(b) and case 2 are eliminated.

7. Person who lives in Kolkata born before M but not immediately before him. Therefore, case 3 is eliminated. Hence, the final arrangement is as follows

 

Hence, M ​lives in Mumbai.

1. X born in a month which have odd number of days but not on even date of a month.

2. Only one person born between X and O.

3. More than three person born between E and the person who lives in Delhi.

 

4. J lives in a city which start with the same alphabetical letter. Therefore, case 1 further divided into two cases.

5. Person who lives in Mumbai born immediately after O.

 

6. Only three person born between R and the person who lives in Patna. Therefore, case 1(b) and case 2 are eliminated.

7. Person who lives in Kolkata born before M but not immediately before him. Therefore, case 3 is eliminated. Hence, the final arrangement is as follows

 

Since, J born on 9 May and R born on 26 March.

Hence, two person born between them which are O and M.

1. X born in a month which have odd number of days but not on even date of a month.

2. Only one person born between X and O.

3. More than three person born between E and the person who lives in Delhi.

 

4. J lives in a city which start with the same alphabetical letter. Therefore, case 1 further divided into two cases.

5. Person who lives in Mumbai born immediately after O.

 

6. Only three person born between R and the person who lives in Patna. Therefore, case 1(b) and case 2 are eliminated.

7. Person who lives in Kolkata born before M but not immediately before him. Therefore, case 3 is eliminated. Hence, the final arrangement is as follows

 

Since, on 9th May J was born and just before him M was born.

1. X born in a month which have odd number of days but not on even date of a month.

2. Only one person born between X and O.

3. More than three person born between E and the person who lives in Delhi.

 

4. J lives in a city which start with the same alphabetical letter. Therefore, case 1 further divided into two cases.

5. Person who lives in Mumbai born immediately after O.

 

6. Only three person born between R and the person who lives in Patna. Therefore, case 1(b) and case 2 are eliminated.

7. Person who lives in Kolkata born before M but not immediately before him. Therefore, case 3 is eliminated. Hence, the final arrangement is as follows

 

Hence, all except O born in the month which have odd number of days.

1. X born in a month which have odd number of days but not on even date of a month.

2. Only one person born between X and O.

3. More than three person born between E and the person who lives in Delhi.

 

4. J lives in a city which start with the same alphabetical letter. Therefore, case 1 further divided into two cases.

5. Person who lives in Mumbai born immediately after O.

 

6. Only three person born between R and the person who lives in Patna. Therefore, case 1(b) and case 2 are eliminated.

7. Person who lives in Kolkata born before M but not immediately before him. Therefore, case 3 is eliminated. Hence, the final arrangement is as follows

 

Since, O born on 9th April and J and E both born in May.

Hence, More than one option is correct.

Given, the persons are O, P, Q, R, S, T, U, V.

1. Only two person sits between U and V.

2. R sits second to the left of U.                        

3. R and P sits opposite to each other and facing opposite direction.

4. As many person sits between S and O as many person sits between S and Q, who sits third to the left of S. So case 1 and case 2 further divided into two more cases.

5. The immediate neighbour of Q faces in opposite direction. So if U faces outside (or inside) the other immediate neighbour of Q faces inside (or outside).

7. The number of person faces away from centre is less than that of faces towards centre. R is not the neighbour of O. Then case 1(b) is eliminated.

8) T and Q faces in same direction but faces opposite direction of P. 

9. No three consecutive person faces in same direction. So, case 2(b) is eliminated.                                        

10. S and V sits immediate left to each other. So, case 2(a) is eliminated. Hence, final arrangement is as follows

Hence, P and U sits adjacent to O.

Given, the persons are O, P, Q, R, S, T, U, V.

1. Only two person sits between U and V.

2. R sits second to the left of U.                        

3. R and P sits opposite to each other and facing opposite direction.

4. As many person sits between S and O as many person sits between S and Q, who sits third to the left of S. So case 1 and case 2 further divided into two more cases.

5. The immediate neighbour of Q faces in opposite direction. So if U faces outside (or inside) the other immediate neighbour of Q faces inside (or outside).

7. The number of person faces away from centre is less than that of faces towards centre. R is not the neighbour of O. Then case 1(b) is eliminated.

8) T and Q faces in same direction but faces opposite direction of P. 

9. No three consecutive person faces in same direction. So, case 2(b) is eliminated.                                        

10. S and V sits immediate left to each other. So, case 2(a) is eliminated. Hence, final arrangement is as follows

When counted from clockwise direction of O only two persons sits between O and S.

Given, the persons are O, P, Q, R, S, T, U, V.

1. Only two person sits between U and V.

2. R sits second to the left of U.                        

3. R and P sits opposite to each other and facing opposite direction.

4. As many person sits between S and O as many person sits between S and Q, who sits third to the left of S. So case 1 and case 2 further divided into two more cases.

5. The immediate neighbour of Q faces in opposite direction. So if U faces outside (or inside) the other immediate neighbour of Q faces inside (or outside).

7. The number of person faces away from centre is less than that of faces towards centre. R is not the neighbour of O. Then case 1(b) is eliminated.

8) T and Q faces in same direction but faces opposite direction of P. 

9. No three consecutive person faces in same direction. So, case 2(b) is eliminated.                                        

10. S and V sits immediate left to each other. So, case 2(a) is eliminated. Hence, final arrangement is as follows

Hence, all except P faces towards the centre.

Given, the persons are O, P, Q, R, S, T, U, V.

1. Only two person sits between U and V.

2. R sits second to the left of U.                        

3. R and P sits opposite to each other and facing opposite direction.

4. As many person sits between S and O as many person sits between S and Q, who sits third to the left of S. So case 1 and case 2 further divided into two more cases.

5. The immediate neighbour of Q faces in opposite direction. So if U faces outside (or inside) the other immediate neighbour of Q faces inside (or outside).

7. The number of person faces away from centre is less than that of faces towards centre. R is not the neighbour of O. Then case 1(b) is eliminated.

8) T and Q faces in same direction but faces opposite direction of P. 

9. No three consecutive person faces in same direction. So, case 2(b) is eliminated.                                        

10. S and V sits immediate left to each other. So, case 2(a) is eliminated. Hence, final arrangement is as follows

Hence, T sits opposite to U.

Given, the persons are O, P, Q, R, S, T, U, V.

1. Only two person sits between U and V.

2. R sits second to the left of U.                        

3. R and P sits opposite to each other and facing opposite direction.

4. As many person sits between S and O as many person sits between S and Q, who sits third to the left of S. So case 1 and case 2 further divided into two more cases.

5. The immediate neighbour of Q faces in opposite direction. So if U faces outside (or inside) the other immediate neighbour of Q faces inside (or outside).

7. The number of person faces away from centre is less than that of faces towards centre. R is not the neighbour of O. Then case 1(b) is eliminated.

8) T and Q faces in same direction but faces opposite direction of P. 

9. No three consecutive person faces in same direction. So, case 2(b) is eliminated.                                        

10. S and V sits immediate left to each other. So, case 2(a) is eliminated. Hence, final arrangement is as follows

Hence, V sits immediate left of S.

Here, we use some notation

Six persons live in a family namely A, K, M, R, T and Y

1. M is the brother – in – law of husband of A’s daughter – in – law. Which means M’s sister is A’s daughter – in – law or A’s son is M’s brother – in – law.

2. T is daughter – in – law of grandparent of K, who is the only niece of R’s brother – in – law . So K is a female.                                             

3. Y is a male person.                                                                                                                                                                     

4. There is no single parents. Since there is two married couple so T must be A’s daughter – in – law  which means T is sister of M and mother of K. Therefore, R is T’s husband and A’s son. Since Y is a male person so A is a female.

Representing this in a family tree we get                                          

Hence, all statements except Y is father of R are false.

Here, we use some notation

Six persons live in a family namely A, K, M, R, T and Y

1. M is the brother – in – law of husband of A’s daughter – in – law. Which means M’s sister is A’s daughter – in – law or A’s son is M’s brother – in – law.

2. T is daughter – in – law of grandparent of K, who is the only niece of R’s brother – in – law . So K is a female.                                             

3. Y is a male person.                                                                                                                                                                     

4. There is no single parents. Since there is two married couple so T must be A’s daughter – in – law  which means T is sister of M and mother of K. Therefore, R is T’s husband and A’s son. Since Y is a male person so A is a female.

Representing this in a family tree we get                                          

Hence, M is the brother - in - law of R.

Here, we use some notation

Six persons live in a family namely A, K, M, R, T and Y

1. M is the brother – in – law of husband of A’s daughter – in – law. Which means M’s sister is A’s daughter – in – law or A’s son is M’s brother – in – law.

2. T is daughter – in – law of grandparent of K, who is the only niece of R’s brother – in – law . So K is a female.                                             

3. Y is a male person.                                                                                                                                                                     

4. There is no single parents. Since there is two married couple so T must be A’s daughter – in – law  which means T is sister of M and mother of K. Therefore, R is T’s husband and A’s son. Since Y is a male person so A is a female.

Representing this in a family tree we get                                          

Hence, T is the mother of K.