SBI PO Prelims Memory Based Paper (Held On: 8 March 2025 Shift 1) (Previous Year Paper)

The correct answer is Option 2.

 

Key Points

• Critics caution against social vices that may accompany online betting, including addiction, financial loss, and deteriorating mental health.
• The passage specifically mentions "addiction" as one of the potential negative impacts of online betting.
• The other options such as loss of personal privacy, reduction in sports popularity, decrease in state revenue, and higher taxes on other forms of entertainment are not mentioned as potential negative impacts in the passage.

Therefore, the correct answer is Option 2.

 

Additional Information

• Option 1: Loss of personal privacy is not mentioned in the passage as a potential negative impact.
• Option 3: Reduction in sports popularity is not discussed as a potential negative impact in the passage.
• Option 4: Decrease in state revenue is not mentioned as a potential negative impact.
• Option 5: Higher taxes on other forms of entertainment is not mentioned as a potential negative impact.

The correct answer is Option 3.

 

Key Points

• Proponents argue that online betting will engage users with a new form of recreational activity.
• They also believe that it will potentially generate substantial revenue through taxation.
• The passage does not mention increasing tourism, reducing crime rates, decreasing the unemployment rate, or promoting traditional sports as reasons cited by proponents.

Therefore, the correct answer is Option 3.

 

Additional Information

• Option 1: Increasing tourism is not mentioned as a reason for lifting the online betting ban.
• Option 2: Reducing crime rates is not cited by proponents in the passage.
• Option 4: Decreasing the unemployment rate is not discussed as a reason for lifting the ban.
• Option 5: Promoting traditional sports is not mentioned as a reason for lifting the online betting ban.

The correct answer is Option 3.

 

Key Points

• The passage explicitly states that individual states now have the autonomy to regulate and legislate online betting within their jurisdictions.
• The removal of the federal ban allows each state to create its own regulations and laws related to online betting.
• This shift is expected to lead to a varied landscape of regulations across the country.
• Critics are concerned about the enforcement and compliance challenges due to different regulations in each state.

Therefore, the correct answer is Option 3.

 

Excerpt from the Passage: "With the ban removed, states now have the autonomy to regulate and legislate online betting within their jurisdictions."

 

Additional Information

• Federal Government: The passage does not indicate that the federal government retains control over online betting regulations.
• All Betting Companies: The passage does not suggest that betting companies themselves have the autonomy to regulate online betting.
• International Bodies: The passage does not mention any international bodies having jurisdiction over online betting in the US.
• The Supreme Court: The passage does not assign regulatory autonomy to the Supreme Court for online betting.

The correct answer is Option 4.

 

Key Points

• States having autonomy to regulate online betting within their jurisdictions is expected to lead to a "patchwork of regulations across the country".
• This decentralized approach means that different states may have varying laws and regulations regarding online betting.
• A patchwork of regulations can complicate enforcement and compliance efforts at the national level.

Therefore, the correct answer is Option 4.

 

Additional Information

• Option 1: A unified national regulation standard is unlikely given that each state has the autonomy to create its own regulations.
• Option 2: Simplified enforcement and compliance efforts are not expected, as differing state laws can complicate these efforts.
• Option 3: The end of match-fixing concerns is not related to state regulatory autonomy and remains a broader issue in sports betting.
• Option 5: An immediate increase in sports viewership is not directly mentioned as an expectation stemming from state-level regulatory autonomy.

The correct answer is Option 2.

 

Key Points

• Statement A: The ban on online betting in the US was removed due to pressure from international sports organizations.
• This statement is not correct as the passage does not mention any such pressure as a reason for lifting the ban.
• Statement B: Critics warn that the removal of the ban may lead to financial ruin for some individuals.
• This statement is correct as it reflects the concerns mentioned by the critics in the passage.
• Statement C: The US has significant experience in regulating online betting activities compared to European countries.
• This statement is not correct as the passage indicates that Europe has had long-standing regulations on online betting, whereas the US is just beginning to navigate this area.

Therefore, the correct statement in the context of the passage is: Only B.

The correct answer is 'Option 1'.

 

Key Points

• A) Online betting has the potential to generate uneven economic benefits across different states.
• This can be inferred from the passage. The passage mentions that states now have the autonomy to regulate and legislate online betting, leading to a patchwork of regulations. This suggests that different states might experience varying economic impacts.
• B) Sports organizations fully support the lifting of the online betting ban in the US.
• This cannot be inferred from the passage. The passage raises concerns about the integrity of sports and the threat of match-fixing, indicating potential opposition from sports organizations.
• C) There will be a uniform response from all states regarding online betting regulations.
• This cannot be inferred from the passage. The passage explicitly mentions a patchwork of regulations across the country, indicating a lack of uniformity.
• D) The majority of Americans are likely to oppose the introduction of online betting.
• This cannot be inferred from the passage. The passage presents both proponents and critics but does not provide data on the majority opinion of Americans.
• E) The challenges faced by European countries in online betting are identical to those faced by the US.
• This cannot be inferred from the passage. The passage suggests that the US can learn from Europe’s experiences, indicating that while there are similarities, the challenges are not necessarily identical.

Therefore, the correct answer is Option 1.

 

Additional Information

• Option 2: Incorrect because the passage indicates potential concerns from sports organizations.
• Option 3: Incorrect because the passage mentions a patchwork of regulations.
• Option 4: Incorrect because the passage does not provide data on the majority opinion of Americans.
• Option 5: Incorrect because the passage indicates differences in challenges between the US and European countries.

The correct answer is 'robust regulatory frameworks to monitor'.

 

Key Points

• European countries have implemented stringent regulatory mechanisms to oversee online betting activities.
• These frameworks aim to balance the economic benefits of online betting while minimizing the associated negative impacts.
• Options 1, 2, 3, and 5 do not comprehensively capture the essence of the regulation and control mentioned in the passage.

Therefore, the correct answer is Option 4.

 

Complete Sentence: "European countries have developed robust regulatory frameworks to monitor and control online betting activities, aiming to mitigate the negative impacts while capitalizing on the economic benefits."

 

Additional Information

• Option 1: "Stringent taxation policies" is incorrect because taxation alone does not cover the comprehensive regulation needed.
• Option 2: "Severe penalties" is incorrect as penalties are part of a regulatory framework, not the entire structure.
• Option 3: "Cutting-edge technology" is incorrect because technology supports but does not constitute the entire regulatory framework.
• Option 5: "Comprehensive advertising strategies" is incorrect as advertising strategies are aimed at promotion rather than regulation.

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

Key Points

• The word "engage" means to attract or hold the attention of someone; to involve someone in an activity. (लुभाना, सम्मिलित करना)
• Example: The teacher used a fun game to engage the students in the lesson.
• "Entice" means to attract or tempt someone by offering pleasure or advantage. (प्रलोभित करना, आकर्षित करना)
• Example: The advertisement is designed to entice people into buying the product.
• Hence, we can infer that a similar meaning of 'engage' is 'entice'.

Therefore, the correct answer is: Option 2 i.e., Entice.

Additional Information

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

• Detach (अलग करना): Disengage something or part of something and remove it.
• Example: Please detach this coupon and bring it to the store.
• Ignore (अनदेखा करना): Refuse to take notice of or acknowledge.
• Example: She chose to ignore the advice of her friends.
• Separate (अलग करना): Cause to move or be apart.
• Example: The kids were separated into different groups for the activity.
• Neglect (उपेक्षा करना): Fail to care for properly.
• Example: He would often neglect his homework to play video games.

The correct answer is: Option 3 i.e., Virtue.

Key Points

• The word "vice" means immoral or wicked behavior. (बुराई)
• Example: Gambling can often lead to vices such as dishonesty and addiction.
• "Virtue" refers to behavior showing high moral standards or a quality considered morally good or desirable. (पुण्य)
• Example: Honesty is a virtue that is highly valued in many cultures.
• Hence, we can infer that the opposite of 'vice' is 'virtue'.

Therefore, the correct answer is: Option 3 i.e., Virtue.

Additional Information

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

• Crime (अपराध): An action or omission that constitutes an offense and is punishable by law.
• Example: He was arrested for committing a serious crime.
• Sin (पाप): An immoral act considered to be a transgression against divine law.
• Example: Many consider lying to be a sin.
• Corruption (भ्रष्टाचार): Dishonest or fraudulent conduct by those in power, typically involving bribery.
• Example: The politician was removed from office due to corruption charges.
• Depravity (भ्रष्टता): Moral corruption; wickedness.
• Example: The story is a tale of human depravity and greed.

The correct answer is option 3.

Key Points

• Part C of the sentence i.e. "the team of experts were" is erroneous.
• Part C of the sentence is incorrect because the subject "team" is singular, so it should be followed by the singular verb "was" instead of the plural verb "were."
• Hence, the correct answer is C.
• The correct sentence would be: "Despite their differing viewpoints on the matter, the team of experts was able to reach an agreement."

The correct answer is option 3.

Key Points

• Part C of the sentence i.e. "and then she is applying" is erroneous.
• The sentence begins in the future tense with "She will finish her degree next year," indicating a future action. To maintain tense consistency, the phrase "is applying" should be replaced with "will apply." This change ensures that the entire sentence is in the future tense, making it grammatically correct.
• Hence, the correct answer is C.
• The correct sentence would be: "She will finish her degree next year, and then she will apply for her dream job."

 

Additional Information

• Let's understand the simple future tense:
• Sentence structure -
• Subject + will/shall + base form of the verb + (complements or additional information)
• For Example -
• She will visit her grandmother tomorrow.
• They shall attend the conference next week.
• He will complete the project by Friday.
• I shall call you later.

The correct answer is option 1.

 Key Points

• Part A of the sentence i.e. "when he was arriving" is erroneous.
• The phrase "was arriving" is in the past continuous tense, but the context of "last night" calls for the use of the past simple tense. Therefore, "was arriving" should be replaced with "arrived" to make the sentence grammatically correct.
• Hence, the correct answer is A.
• The correct sentence would be: "When he arrived at the party last night, she said she loved the gift, but now she regrets it deeply."

 

 Additional Information

Let's understand past simple and past continuous tense:

• Past Simple Tense Structure:
• Subject + Verb (in past simple form) + Rest of the Sentence
• Indicators of Past Simple Tense:
• Specific time expressions (e.g., yesterday, last night, in 1999).
• Regular verbs with -ed endings (e.g., walked, talked).
• Irregular verbs (e.g., went, ate) that change form to indicate the past.
• Signal words like "once," "twice," "before," or "after."
• For Example:
• She visited the museum yesterday. (Specific time - yesterday)
• He played basketball with his friends last night. (Specific time - last night)
• They went to the beach last summer. (Specific time - last summer)
• I read that book once. (Signal word - once)
• Past Continuous Tense Structure:
• Subject + Was/Were + Verb (ending in -ing) + Rest of the Sentence
• Indicators of Past Continuous Tense:
• The verb "was" or "were" (indicating past tense).
• A verb ending in -ing (present participle form).
• Indications of actions in progress at a specific time or duration in the past.
• For Example:
• He was studying all night. (Action in progress at a specific time - all night)
• They were playing soccer when it started raining. (Action in progress at a specific time - when it started raining)
• She was working on her project for hours. (Duration in the past - for hours)
• I was reading a book while waiting for the train. (Action in progress at a specific time - while waiting for the train)

The correct answer is option 1.

 Key Points

• Part A of the sentence i.e. "If I will win the lottery" is erroneous.
• Here, "will win" should be replaced with "win" to make the sentence grammatically correct. In conditional statements like this, we use the simple present tense ("win") in the if-clause and the future tense ("will") in the result clause.
• Hence, the correct answer is A.
• The correct sentence would be: "If I win the lottery, I will buy a new car, travel the world, and live in luxury."

 

 Additional Information

Let's understand different types of conditional sentences - 

• The Zero Conditional - General truth
• Sentence structure - If + present simple, present simple 
• For Example -
• If I get a cup of coffee in the morning, I feel energetic all day.
• The First Conditional - Future event
• Sentence structure - If + present simple, will + infinitive 
• For Example -
• "If I have a test tomorrow, I will study all night.".
• The Second Conditional - Hypothetical outcome
• Sentence structure - if + past simple, would + infinitive 
• For Example -
• If I had a million dollars, I would buy an island.
• The Third Conditional - Hypothetical outcome
• Sentence structure - if + past perfect, would + have + past participle 
• For Example -
• If I had taken my medicine on time, I wouldn't have gotten sick.

The correct answer is option 5.

 Key Points 

• This sentence is error-free and it discusses the potential negative effects of constant exposure to noise, including increased stress levels, anxiety, irritability, and cognitive impairment.
• Hence, the correct answer is E.
• Let's understand some important vocab given in the sentence:
• Constant - continuous; without interruption (निरंतर)
• For Example -
• The constant noise from the construction site was bothering the residents.
• Exposure - the state of being in contact with something, especially something harmful or unpleasant (अनावरण)
• For Example -
• Prolonged exposure to the sun can lead to skin damage.
• Stress levels - the amount of stress experienced by an individual (तनाव स्तर)
• For Example -
• Her stress levels have been high due to the workload.
• Anxiety - a feeling of unease, such as worry or fear, that can vary in intensity (चिंता)
• For Example -
• He experienced anxiety before his job interview.
• Irritability - the state of being easily annoyed or provoked (चिढ़ापन)
• For Example -
• Lack of sleep can lead to irritability.
• Cognitive impairment - a decline in cognitive function, including memory, thinking, and reasoning (मानसिक शक्ति में कमी)
• For Example -
• Older adults may experience cognitive impairment as they age.

The correct answer is option 2.

Key Points

• Part B of the sentence i.e. "most expensive spice worldwide" is erroneous.
• Part B of the sentence is incorrect because it uses the singular form "spice" instead of the plural form "spices." Since the sentence refers to saffron as one of the most expensive spices worldwide, it should use the plural form to match the context correctly.
• Hence, the correct answer is B.
• The correct sentence would be: "Saffron is one of the most expensive spices in the world, it is valued for its culinary and medicinal value."

The correct answer is option 2.

Key Points

• Part B of the sentence i.e. "alterations with our lifestyle" is erroneous.
• The preposition "with" should be replaced with "to" to make the sentence grammatically correct.
• The correct phrase is "alterations to our lifestyle" because we are talking about changes made in our lifestyle to achieve a goal. So, it should be "alterations to our lifestyle" instead of "alterations with our lifestyle."
• Hence, the correct answer is B.
• The correct sentence would be: "These are just small alterations to our lifestyle that will help us achieve that perfect body."

The correct answer is 'Only E-C and F-B'.

Key Points 

• The institution was sanctioned by the U.N. Security Council last year as a part of global efforts.
• Fragment B of column 1 is matched with fragment F of column 2 to make the sentence contextually and grammatically correct.
• This week's summit is intended to craft concrete steps to implement the Panmunjom Declaration, named after the border village.
• Fragment C of column 1 is matched with fragment E of column 2 to make the sentence contextually and grammatically correct.
• Therefore 'Only E-C and F-B' make valid combinations.

Hence option 5 is correct.

Additional Information

• ​The latest summit among USA and North Korea will be a litmus test for the stalled negotiations on the nuclear programme of North Korea.
• Fragment A of column 1 is matched with fragment D of column 2 to make the sentence contextually correct but it is grammatically erroneous.
• Among is used for more than two objects whereas here only two nouns i.e. North Korea and USA is given.
• Thus use of "between" is preferred.
• The correct sentence would be: The latest summit between USA and North Korea will be a litmus test for the stalled negotiations on the nuclear programme of North Korea.

The correct answer is option 4.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (1):

Are we, as a society, (1) public rudeness?

• This sentence suggests a reflection on society's stance or attitude towards public rudeness.
• Blank (1) should be filled with a word indicating whether society is accepting or condemning public rudeness.
• Now, let's understand the meanings of the given words as options:
• Denouncing - publicly declare to be wrong or evil; criticize or condemn strongly (निन्दा करना)
• For Example -
• The community leaders are denouncing the divisive rhetoric for the sake of unity and harmony.
• Rejecting - refusing to accept or consider; discarding as unacceptable (अस्वीकृति करना)
• For Example -
• Despite the attractive offer, she was firm in rejecting the job offer due to the long working hours.
• Repelling - driving away or resisting an attack or assailant; causing strong dislike or disgust (हटाना या विरोध करना)
• For Example -
• The strong smell of the chemical cleaner was repelling, making it difficult for people to stay in the room.
• Condoning - accepting, allowing, or approving something, especially with reluctance; overlooking or forgiving an offence (समर्थन करना)
• For Example -
• By not taking any action against the employee's unethical behaviour, the manager seemed to be condoning such actions in the workplace.
• Enhancing - intensifying, improving, or increasing the quality, value, or attractiveness of something (बढ़ावा देना)
• For Example -
• Regular exercise is known for enhancing overall health and well-being.
• So, given the context, the most appropriate word to fill in the blank labelled as (1) is "condoning." The sentence is questioning whether society is accepting or allowing public rudeness, making "condoning" the suitable choice.
• Therefore, the correct answer is "condoning."
• The complete sentence would be: "Are we, as a society, condoning public rudeness?"

The correct answer is option 1.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (2):

So much so, that a polite word from a stranger or a show of (2) in a supermarket comes as a pleasant shock!

• This sentence conveys the idea that encountering politeness or consideration in a supermarket is surprising.
• Blank (2) should be filled with a word conveying the idea of politeness or consideration.
• Now, let's understand the meanings of the given words as options:
• Consideration - thoughtfulness and sensitivity towards others (सोच-विचार)
• For Example -
• Her consideration of others' feelings reflects her thoughtfulness and sensitivity in every interaction.
• Exaggeration - a statement that represents something as better or worse than it really is; overstatement (अतिशयोक्ति)
• For Example -
• Her description of the incident seemed like an exaggeration, as the reality was not as dramatic as she portrayed.
• Proliferation - rapid increase in numbers; multiplication (विकास)
• For Example -
• The proliferation of technology in recent years has transformed the way we live and work.
• Extravagance - the quality of exceeding the bounds of reason or necessity; excessive spending or actions (अत्यधिकता)
• For Example -
• Her lifestyle reflected an undeniable extravagance, adorned with luxurious possessions and opulent experiences.
• Flamboyance - a tendency to attract attention because of one's exuberance, confidence, and stylishness (चमकीलापन)
• For Example -
• The actor's flamboyance on the red carpet made him stand out at the awards ceremony.
• So, given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (2) is "consideration." It aligns with the idea that encountering a polite word or a show of careful thought in a supermarket is surprising.
• Therefore, the correct answer is "consideration."
• The complete sentence would be: "So much so, that a polite word from a stranger or a show of consideration in a supermarket comes as a pleasant shock!"

The correct answer is option 2.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (3):

This insensitivity to others, deepened by self-preoccupation, is a symptom of a dangerous lack of (3) kindness.

• This sentence suggests that insensitivity to others is a symptom of a dangerous lack of inherent or natural kindness.
• Blank (3) should be filled with a word indicating inborn or natural.
• Now, let's understand the meanings of the given words as options:
• Resilient - able to withstand or recover quickly from difficult conditions; tough (सहनशील)
• For Example -
• Despite facing numerous setbacks, the resilient athlete continued to train hard and eventually achieved success.
• Innate - existing from birth; inborn; natural (सहज)
• For Example -
• Her innate talent for playing the piano became evident at a very young age.
• Enigmatic - mysterious, puzzling, difficult to understand or interpret (रहस्यमय)
• For Example -
• The ancient artefact's enigmatic symbols left archaeologists puzzled about their meaning.
• Ineffable - too great or extreme to be expressed or described in words; beyond expression (अवाच्य)
• For Example -
• The beauty of the sunset over the mountains was ineffable, leaving everyone in awe-struck silence.
• Invasive - tending to spread aggressively; intrusive (आक्रमक)
• For Example -
• The invasive species of plants quickly overtook the native flora, causing ecological imbalances.
• So, given the context, the most appropriate option to fill in the blank labelled as (3) is "innate." It aligns with the idea that insensitivity to others is a result of a dangerous lack of inherent or natural kindness.
• Therefore, the correct answer is "innate."
• The complete sentence would be: "This insensitivity to others, deepened by self-preoccupation, is a symptom of a dangerous lack of innate kindness."

The correct answer is option 3.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (4):

Not a moment can be spared for the person seated inches away, perhaps a first-time traveller struggling with a seat belt! Whether plain old-fashioned kindness, a golden (4)?

• This sentence suggests the need for a term that represents a positive and valuable quality associated with kindness.
• Blank (4) should be filled with a word that refers to a quality associated with kindness.
• Now, let's understand the meanings of the given words as options:
• Aversion - a strong dislike or a feeling of repugnance (घृणा)
• For Example -
• His aversion to public speaking made it difficult for him to address a large audience.
• Harmony - the state of being in agreement or concord; a pleasing arrangement or combination of different elements (सामंजस्य)
• For Example -
• The musicians worked together in perfect harmony to create a beautiful symphony.
• Virtue - behaviour showing high moral standards; a quality or trait considered as good (गुण)
• For Example -
• Honesty and integrity are virtues that are highly valued in any ethical society.
• Apathy - lack of interest, enthusiasm, or concern; indifference (उदासीनता)
• For Example -
• The students' apathy towards the school assembly was evident in their disengaged expressions.
• Deception - the action of deceiving someone; the act of misleading or causing someone to believe something that is not true (छल)
• For Example -
• The magician's skilful deception left the audience in awe and wonder.
• So, considering the context and the positive connotation associated with kindness, the most appropriate option to fill in the blank labelled as (4) is "virtue." It aligns with the idea that kindness is not just a simple act but a golden quality or trait that is morally good.
• Therefore, the correct answer is "virtue."
• The complete sentence would be: "Not a moment can be spared for the person seated inches away, perhaps a first-time traveller struggling with a seat belt! Whether plain old-fashioned kindness, a golden virtue?"

The correct answer is option 5.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (5):

Often it takes courage to be kind because with it goes the risk of being rejected, perhaps even cheated when you let your guard down to assist another person out of sheer goodwill or (5).

• This sentence highlights that being kind involves the risk of potential rejection or even being taken advantage of when helping someone with genuine goodwill.
• Blank (5) should be filled with a word conveying a positive quality, like goodwill.
• Now, let's understand the meanings of the given words as options:
• Intricacy - complex, detailed, and involved; having many interconnected parts (जटिलता)
• For Example -
• The intricacy of the artist's masterpiece amazed everyone, as they marvelled at the tiny details that brought the painting to life.
• Ambiguity - the quality of being open to more than one interpretation; inexactness (अस्पष्टता)
• For Example -
• The artist intentionally infused the painting with ambiguity, inviting diverse interpretations from viewers.
• Animosity - strong hostility or antagonism; active hatred (शत्रुता)
• For Example -
• The animosity between the rival teams was evident on the field, with players engaging in heated confrontations throughout the match.
• Tenacity - the quality or fact of being very determined; persistence (दृढ़ता)
• For Example -
• Despite facing numerous challenges, her tenacity and unwavering commitment to her goals allowed her to overcome obstacles and succeed.
• Sympathy - feelings of pity and sorrow for someone's misfortune; understanding between people; common feeling (सहानुभूति)
• For Example -
• The teacher expressed sympathy for the students going through a tough time and offered support to help them cope with the difficulties they were facing.
• So, considering the context, the most appropriate option to fill in the blank labelled as (5) is "sympathy." It aligns with the idea that there is a risk of being rejected or cheated when one lets their guard down to assist another person out of goodwill or sympathy.
• Therefore, the correct answer is "sympathy."
• The complete sentence would be: "Often it takes courage to be kind because with it goes the risk of being rejected, perhaps even cheated when you let your guard down to assist another person out of sheer goodwill or sympathy."

The correct answer is option 2.

Key Points

To answer this question, let's first understand the context of the sentence containing the blank labelled as (6):

If you needed help and people walked by with eyes (6)…what then?

• This sentence suggests a scenario where someone requires assistance, and people are passing by without offering help.
• Blank (6) should be filled with a word conveying the idea of avoiding eye contact or not showing any concern.
• Now, let's understand the meanings of the given words as options:
• Engrossed - completely absorbed or immersed in something; having one's attention fully captivated (रुचित)
• For Example -
• She was so engrossed in her book that she didn't notice the time passing by.
• Averted - turned away or prevented (टाला गया)
• For Example -
• The disaster was averted due to the timely intervention of the emergency response team.
• Pondered - thought about something carefully and thoroughly (विचार किया)
• For Example -
• He pondered over the decision for days before finally making up his mind.
• Focused - concentrated attention or effort on a particular task or objective (केंद्रित)
• For Example -
• To excel in the exam, she focused on studying consistently throughout the semester.
• Flinched - make a quick, nervous movement of the face or body as an instinctive reaction to surprise, fear, or pain (चौंकना)
• For Example -
• He flinched when he heard the sudden loud noise, showing his startled reaction.
• So, given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (6) is "averted." It aligns with the idea that people are walking by without offering help and possibly avoiding eye contact or turning away.
• Therefore, the correct answer is "averted."
• The complete sentence would be: "If you needed help and people walked by with eyes averted…what then?"

The correct answer is **'one of those players who have'**​

Key Points

• 'one of those players who have' will replace 'one of those players who has'.
• In the question, 'players' is written after 'one of'. 'Players' is plural. Therefore, the verb that will agree will also be plural and hence 'have' will be appropriate.
• The verb have, which is a be verb in the sentence is agreeing with players. Therefore, it will take a plural form.
• Therefore, the correct answer is: He is one of those players who have won many accolades in such a short time.

​

 

• Don't confuse the aforementioned question with sentences like:
• One of the boys has come to the party- referring to a single boy
• One of the players is injured- referring to a single player

The correct answer is dying of.

​

Key Points

• 'dying of' will replace 'dying from'.
• dying of is used in case of someone dying of a disease.
• For example: He died of cancer.
• Therefore, the correct answer is: The doleful news of the boy dying of malaria brought about an envelope of gloom in the locality.
• dying from is used in case of someone dying from an incident or event.
• For example: He died from an accident.

Additional Information

• doleful- mournful
• gloom- lowness of spirits; dejection

The correct answer is had asked him.

Key Points

• 'had asked him' will replace 'would've asked him'.
• The aforementioned sentence is a conditional sentence. A conditional sentence is one in which if is used.
• The three types of conditional sentences (with examples) are given in the table.

 

 

• In a sentence like this, when 'if' is used, it always agrees with the past perfect tense.
• The incident that happens first or was supposed to happen first takes a past perfect tense.
• For example: I would've passed if I had studied.
• ​Therefore, the correct answer is: I am certain that Subham would've lent you money if you had asked him.

Important Points

• Even if the sentence is reversed, the tense form of the sentence wouldn't change.
• For example: If you had come yesterday, you would've met the guest of honour.

The correct answer is 'will have written'.

Key Points

• The given sentence is in the future perfect tense.
• Future perfect Tense is when action will have been completed in the future.
• The structure is as follows:
• ​Sub + will/shall + have + V3 + obj.
• Thus, 'will have written' will be used instead of 'will have wrote' to make the sentence grammatically correct.
• Hence, option 3 is the most appropriate choice.

The correct sentence will be: 'I will have written articles on different topics before you come.'

Additional Information

• Structure- By the time simple present, future perfect.
• For eg.-  By the time I reach the station, the bus will have arrived.

The correct answer is 'centuries of history'.

Key Points

• The error is in the usage of 'century' in the underlined part.
• Here, the sentence talks about the rich culture, history, and tradition of India.
• 'Century' is in the singular form which means a period of one hundred years.
• The correct word for the underlined part must be 'Centuries' because India's history spans many many years, not just one century.
• 'Century' must be replaced with 'Centuries'. 

Thus the correct sentence is - India is a country of rich culture and has centuries of history and tradition of its own. 

Additional Information

• Option 1 and 3 are grammatically incorrect. 'History' means 'the past considered as a whole'. As India is singular, 'history' must also be singular.

The correct answer is Option 2.

Key Points

• The first sentence in correct sequence of the paragraph is a sentence that introduces a person, situation, or a concept. Hence, the first sentence would be C.
• This statement discusses the concept of ‘women empowerment’ and its importance in society. The second sentence must be D as it carries the idea of ‘women empowerment’ forward. It supports the first sentence as it discusses why women empowerment is important for equality. Note that the pronoun ‘it’ refers to ‘women empowerment’ mentioned in C.
• The third sentence will be B, as it uses the connective ‘But’. Therefore, the sentence follows logically as it tells about the possible problems faced while dealing with issues of women empowerment after having told about the necessity to promote ‘women empowerment’.
• The fourth sentence in the sequence would be E, as it complements the third sentence and provides scope for further discussion as it reassures that efforts are constant in the direction to achieve the goals.
• A informs about these ‘efforts’ and follows E in the sequence.
• The last sentence should conclude the paragraph. This is done by F which expands on the previous sentence and comes as a consequence of A. Hence, the last sentence will be F. It elaborates on why girl child education scheme will lead to equal society.

The correct order after rearrangement is CDBEAF.

The first sentence after rearrangement is C.

The correct answer is Option 1.

Key Points

• The first sentence in correct sequence of the paragraph is a sentence that introduces a person, situation, or a concept. Hence, the first sentence would be C.
• This statement discusses the concept of ‘women empowerment’ and its importance in society. The second sentence must be D as it carries the idea of ‘women empowerment’ forward. It supports the first sentence as it discusses why women empowerment is important for equality. Note that the pronoun ‘it’ refers to ‘women empowerment’ mentioned in C.
• The third sentence will be B, as it uses the connective ‘But’. Therefore, the sentence follows logically as it tells about the possible problems faced while dealing with issues of women empowerment after having told about the necessity to promote ‘women empowerment’.
• The fourth sentence in the sequence would be E, as it complements the third sentence and provides scope for further discussion as it reassures that efforts are constant in the direction to achieve the goals.
• A informs about these ‘efforts’ and follows E in the sequence.
• The last sentence should conclude the paragraph. This is done by F which expands on the previous sentence and comes as a consequence of A. Hence, the last sentence will be F. It elaborates on why girl child education scheme will lead to equal society.

The correct order after rearrangement is CDBEAF.

The third sentence after rearrangement is B.

The correct answer is Option 4.

Key Points

• The first sentence in correct sequence of the paragraph is a sentence that introduces a person, situation, or a concept. Hence, the first sentence would be C.
• This statement discusses the concept of ‘women empowerment’ and its importance in society. The second sentence must be D as it carries the idea of ‘women empowerment’ forward. It supports the first sentence as it discusses why women empowerment is important for equality. Note that the pronoun ‘it’ refers to ‘women empowerment’ mentioned in C.
• The third sentence will be B, as it uses the connective ‘But’. Therefore, the sentence follows logically as it tells about the possible problems faced while dealing with issues of women empowerment after having told about the necessity to promote ‘women empowerment’.
• The fourth sentence in the sequence would be E, as it complements the third sentence and provides scope for further discussion as it reassures that efforts are constant in the direction to achieve the goals.
• A informs about these ‘efforts’ and follows E in the sequence.
• The last sentence should conclude the paragraph. This is done by F which expands on the previous sentence and comes as a consequence of A. Hence, the last sentence will be F. It elaborates on why girl child education scheme will lead to equal society.

The correct order after rearrangement is CDBEAF.

The fourth sentence after rearrangement is E.

The correct answer is Option 3.

Key Points

• The first sentence in correct sequence of the paragraph is a sentence that introduces a person, situation, or a concept. Hence, the first sentence would be C.
• This statement discusses the concept of ‘women empowerment’ and its importance in society. The second sentence must be D as it carries the idea of ‘women empowerment’ forward. It supports the first sentence as it discusses why women empowerment is important for equality. Note that the pronoun ‘it’ refers to ‘women empowerment’ mentioned in C.
• The third sentence will be B, as it uses the connective ‘But’. Therefore, the sentence follows logically as it tells about the possible problems faced while dealing with issues of women empowerment after having told about the necessity to promote ‘women empowerment’.
• The fourth sentence in the sequence would be E, as it complements the third sentence and provides scope for further discussion as it reassures that efforts are constant in the direction to achieve the goals.
• A informs about these ‘efforts’ and follows E in the sequence.
• The last sentence should conclude the paragraph. This is done by F which expands on the previous sentence and comes as a consequence of A. Hence, the last sentence will be F. It elaborates on why girl child education scheme will lead to equal society.

The correct order after rearrangement is CDBEAF.

The last sentence after rearrangement is F.

The correct answer is Option 1.

Key Points

• The first sentence in correct sequence of the paragraph is a sentence that introduces a person, situation, or a concept. Hence, the first sentence would be C.
• This statement discusses the concept of ‘women empowerment’ and its importance in society. The second sentence must be D as it carries the idea of ‘women empowerment’ forward. It supports the first sentence as it discusses why women empowerment is important for equality. Note that the pronoun ‘it’ refers to ‘women empowerment’ mentioned in C.
• The third sentence will be B, as it uses the connective ‘But’. Therefore, the sentence follows logically as it tells about the possible problems faced while dealing with issues of women empowerment after having told about the necessity to promote ‘women empowerment’.
• The fourth sentence in the sequence would be E, as it complements the third sentence and provides scope for further discussion as it reassures that efforts are constant in the direction to achieve the goals.
• A informs about these ‘efforts’ and follows E in the sequence.
• The last sentence should conclude the paragraph. This is done by F which expands on the previous sentence and comes as a consequence of A. Hence, the last sentence will be F. It elaborates on why girl child education scheme will lead to equal society.

The correct order after rearrangement is CDBEAF.

The second sentence after rearrangement is D.

The correct answer is BAC.

Key Points

• Economic: financial or monetary
• Important: main or chief
• Private: personal or one's own

Important Points

We may consider A, B, and C to be three blanks. A is the first blank, B is the second, and C is the third.

• The word 'important', which is an 'adjective', should be chosen for the first blank because the word 'determinant' is a noun.
• The word 'economic' is appropriate for the second blank because an adjective is required to qualify the word 'buoyancy' which is a noun. Thus, the correct choice is 'economic'.
• The word 'private' is appropriate for the last blank because the word 'investment' is a noun and the word 'private' is an adjective and it should be used before the word 'investment'.

The correct sentence will be: The most important determinant of economic buoyancy in India is private investment.

The correct answer is BAC.

Key Points

• Measures**:** actions
• Urged**:** advised
• Reduce**:** lessen or make smaller

Important Points

We may consider A, B, and C to be three blanks. A is the first blank, B is the second, and C is the third.

• The word 'has' is used before the first blank so, the past participle form of the verb('verb³') should be used. The word 'urged' which is the 'verb³' form should be the correct choice.
• The word 'measures' is appropriate for the second blank because the states were urged to take actions to solve some problems.
• The word 'reduce' is appropriate for the third blank because the states were advised to take action to solve an issue.

The correct sentence will be: The Niti Aayog has also urged all states to take measures to reduce the logistics cost of business.

The correct answer is BCA.

Key Points

• Ambitious**:** having strong desire to succeed or determined
• Produce**:** to make
• Renewable**:** capable of being renewed

Important Points

We may consider A, B, and C to be three blanks. A is the first blank, B is the second, and C is the third.

• The base form of the verb('Verb¹') is required for the first blank because the preposition 'to' is used before it. The word 'produce' is 'verb¹' and it is appropriate for the first blank.
• An adjective is required for the second blank to qualify the noun 'power'. The word 'renewable' is appropriate to describe the word 'power'.
• The word 'ambitious' is suitable for the third blank. According to the sentence, whatever India has planned to achieve is certainly an ambitious goal. Hence, the correct choice is 'ambitious'.

The correct sentence will be: India has a plan to produce about 450 gigawatts of renewable power by 2030; it’s a very ambitious goal.

The correct answer is option 5) i.e. impacted, entire.

Key Points

• From the context of the sentence, the adjectives should be used in the given blanks.
• Let us explore the options:
• The first option is incorrect as 'impacting' is used as a third-person form of the verb in the sentence. 'Entiring' is an incorrect word.
• The second option is incorrect as 'impact' is used as a noun. 'Entire' is still okay for the second blank but 'impact' is not fit for the first blank.
• The third option is incorrect as 'impacts' is used as a noun. 'Entered' is used as a past form of the verb 'enter' which is not correct as per the context.
• The fourth option is incorrect as 'enter' is used as a base form of the verb which means come or go into (a place) is correct as per the context. 'Impacted' is still okay for the first blank but 'enter' is not fit for the second blank.
• The fifth option is correct as 'impacted' is used as an adjective to describe the noun 'segments' and 'entire' is also used as an adjective describing the noun 'automotive'.
• Hence, the correct option is "impacted, entire".

​Complete Sentence: The automobile dealerships are among the worst impacted segments within the entire automotive value chain, ICRA said in a statement.

Additional Information

• Important Tips and Tricks to solve double fillers: 
• Do not read options: Read the sentence and think of a word that 'fits' the sentence. Now go to the options and choose the word that best replaces the word that you had thought of initially.
• Elimination method: In certain questions, our knowledge and understanding of vocabulary and common idioms-phrases may be tested. Hence, be sure to have a good skill set of such phrases.
• Use grammar clues: Keep a close watch at the tense of the sentence, subject-verb agreement, whether the blank in the sentence is after the article 'an' etc.
• Use Connotation: Each word expresses two things: a definition and a connotation. A connotation is a positive, negative, or neutral feeling that is implied by or associated with a word.
• Identify the Indicators: Indicators tell us what is coming up. They indicate if the question is moving to draw a contrast with something stated previously, or support something stated previously.

The correct answer is option 1) i.e. uniform, issued.

Key Points

• From the context of the sentence, an adjective and a verb should be used in the given blanks.
• Let us explore the options:
• The first option is correct as 'uniform' is used as an adjective describing the noun 'specification'. 'Issued' is the past participle of the verb used correctly as the sentence is in the present perfect passive voice.
• The second option is incorrect as 'uniformly' is used as an adverb. 'Issued' is still okay for the second blank but 'uniformly' is not fit for the first blank.
• The third option is incorrect as 'issue' is the base form of the verb. 'Uniform' is still okay for the first blank but 'issue' is not fit for the second blank.
• The fourth option is incorrect as 'uniformity' is a noun that means the quality or state of being uniform and is not correct as per the context. 'Issues' is used as a third-person singular form of the verb.
• The fifth option is incorrect as 'uninformed' is used as a verb and 'issue' is the base form of the verb.
• Hence, the correct option is "uniform, issued".

​Complete Sentence: Besides, the uniform specification for food-grains has been issued for paddy procurement.

Additional Information

• Important Tips and Tricks to solve double fillers: 
• Do not read options: Read the sentence and think of a word that 'fits' the sentence. Now go to the options and choose the word that best replaces the word that you had thought of initially.
• Elimination method: In certain questions, our knowledge and understanding of vocabulary and common idioms-phrases may be tested. Hence, be sure to have a good skill set of such phrases.
• Use grammar clues: Keep a close watch at the tense of the sentence, forms of the verb, subject-verb agreement, whether the blank in the sentence is after the article 'an' etc.
• Use Connotation: Each word expresses two things: a definition and a connotation. A connotation is a positive, negative, or neutral feeling that is implied by or associated with a word.
• Identify the Indicators: Indicators tell us what is coming up. They indicate if the question is moving to draw a contrast with something stated previously, or support something stated previously.

The correct answer is option 4) i.e. stopping, stock.

Key Points

• From the context of the sentence, a verb and a noun should be used respectively in the given blanks.
• Let us explore the options:
• The first option is incorrect as 'stopped' is used as a past form of the verb in the sentence. 'Stock' is still okay for the second blank but 'stopped' is not fit for the first blank.
• The second option is incorrect as 'stocked' is used as a verb. 'Stopping' is still okay for the first blank but 'stocked' is not fit for the second blank.
• The third option is incorrect as 'stops' is used as a third-person singular form of the verb. 'Stocking' is used as a verb.
• The fourth option is correct as 'stopping' is used as a present participle form of the verb as the sentence is in the present continuous tense and 'stock' is used as a noun means the capital raised by a company or corporation through the issue and subscription of shares.
• The fifth option is incorrect as 'stop' is used as the base form of the verb and 'stocker' is also used as a noun which is not correct as per the context.
• Hence, the correct option is "stopping, stock".

​Complete Sentence: India’s shrinking economy is not stopping foreign investors from pouring money into the nation’s stock betting on a recovery.​

Additional Information

• Important Tips and Tricks to solve double fillers: 
• Do not read options: Read the sentence and think of a word that 'fits' the sentence. Now go to the options and choose the word that best replaces the word that you had thought of initially.
• Elimination method: In certain questions, our knowledge and understanding of vocabulary and common idioms-phrases may be tested. Hence, be sure to have a good skill set of such phrases.
• Use grammar clues: Keep a close watch at the tense of the sentence, subject-verb agreement, whether the blank in the sentence is after the article 'an' etc.
• Use Connotation: Each word expresses two things: a definition and a connotation. A connotation is a positive, negative, or neutral feeling that is implied by or associated with a word.
• Identify the Indicators: Indicators tell us what is coming up. They indicate if the question is moving to draw a contrast with something stated previously, or support something stated previously.

The correct answer is option 2.

Key Points

• To answer this question, let's understand the meaning of all the given idioms -
• Break the ice - to initiate or start a conversation or social interaction to make others feel more comfortable.
• For Example -
• Sarah told a joke to break the ice at the party, and soon everyone was laughing and chatting.
• Kick the bucket - to die
• For Example -
• Unfortunately, after years of battling illness, she finally kicked the bucket yesterday.
• Cross the Rubicon - passing a point of no return or making an irreversible decision.
• For Example -
• Once she confronted her fears and quit her job, she knew she had crossed the Rubicon.
• Burn the midnight oil - to work late into the night, often referring to studying or working diligently on a task.
• For Example -
• Despite feeling exhausted, she burned the midnight oil to finish her research paper before the deadline.
• Spill the beans - to reveal a secret or disclose confidential information
• For Example -
• I can't believe you spilled the beans about the surprise party! It was supposed to be a secret.
• Therefore, after looking at the meaning of all the given idioms, we can conclude that the idiom 'break the ice' refers to overcoming initial tension or awkwardness, typically in social situations, whereas 'cross the Rubicon' signifies a decisive and irreversible action or commitment, which better captures the significant career change described.
• The correct sentence would be, 'After years of contemplation, she decided to cross the Rubicon and quit her stable job to pursue her dream of becoming an artist.'

General Solution:

From the table:

Public sector employees in Building A = 120

Public sector employees in Building B = a

Public sector employees in Building C = 90

Public sector employees in Building D = 2a

Total public sector employees =120 + a + 90 + 2a = 300

210 + 3a = 300

3a = 90

a = 30

Building A:

Public sector employees = 120

Ratio of public to private = 3 : 2

Private sector employees = 2/3 × 120 = 80

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

120 + 80 + 0.20F = F

200 = 0.80F

F = 250

Total flats in Building A = 250

Building B:

Public sector employees =a = 30

Ratio of public to private = 3 : 5

Private sector employees = 5/3 × 30 = 50

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

30 + 50 + 0.20F = F

80 = 0.80F

F = 100

Total flats in Building B = 100

Building C:

Public sector employees = 90

Ratio of public to private = 2 : 3

Private sector employees = 3/2 × 90 = 135

Vacant flats = 25% of total flats

Let total flats = F

Vacant flats = 0.25F

Total flats = Public + Private + Vacant

90 + 135 + 0.25F = F

225 = 0.75F

F = 300

Total flats in Building C = 300

Building D:

Public sector employees = 2a = 60

Ratio of public to private = 5 : 4

Private sector employees = 4/5 × 60 = 48

Vacant flats = 55% of total flats

Let total flats = F

Vacant flats = 0.55F

Total flats = Public + Private + Vacant

60 + 48 + 0.55F = F

108 = 0.45F

F = 240

Total flats in Building D = 240

Thus,

 

Calculations:

Building C:

Private sector employees in Building C = 135

40% of private sector employees move to Building D:

0.40 × 135 = 54

New private sector employees in Building C:

135 - 54 = 81

Building D:

Private sector employees in Building D = 48

54 private sector employees move from Building C to Building D:

48 + 54 = 102

New private sector employees in Building D: 102

Building A:

Public sector employees in Building A = 120

25% of public sector employees move to Building B:

0.25 × 120 = 30

New public sector employees in Building A:

120 - 30 = 90

Building B:

Public sector employees in Building B = 30

30 public sector employees move from Building A to Building B:

30 + 30 = 60

New public sector employees in Building B: 60

Building C:

Public sector employees in Building C = 90 (unchanged)

Private sector employees in Building C = 81 (updated)

Vacant flats in Building C = 75 (unchanged)

Total occupied flats in Building C = Public + Private

90 + 81 = 171

Building D:

Public sector employees in Building D = 60 (unchanged)

Private sector employees in Building D = 102 (updated)

Vacant flats in Building D = 132 (unchanged)

Total occupied flats in Building D = Public + Private

60 + 102 = 162

Ratio = Total occupied flats in Building C / Total occupied flats in Building D = 171 / 162

171:162 = 19:18

Thus, the new ratio of total occupied flats in Building C to Building D is 19:18.

General Solution:

From the table:

Public sector employees in Building A = 120

Public sector employees in Building B = a

Public sector employees in Building C = 90

Public sector employees in Building D = 2a

Total public sector employees =120 + a + 90 + 2a = 300

210 + 3a = 300

3a = 90

a = 30

Building A:

Public sector employees = 120

Ratio of public to private = 3 : 2

Private sector employees = 2/3 × 120 = 80

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

120 + 80 + 0.20F = F

200 = 0.80F

F = 250

Total flats in Building A = 250

Building B:

Public sector employees =a = 30

Ratio of public to private = 3 : 5

Private sector employees = 5/3 × 30 = 50

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

30 + 50 + 0.20F = F

80 = 0.80F

F = 100

Total flats in Building B = 100

Building C:

Public sector employees = 90

Ratio of public to private = 2 : 3

Private sector employees = 3/2 × 90 = 135

Vacant flats = 25% of total flats

Let total flats = F

Vacant flats = 0.25F

Total flats = Public + Private + Vacant

90 + 135 + 0.25F = F

225 = 0.75F

F = 300

Total flats in Building C = 300

Building D:

Public sector employees = 2a = 60

Ratio of public to private = 5 : 4

Private sector employees = 4/5 × 60 = 48

Vacant flats = 55% of total flats

Let total flats = F

Vacant flats = 0.55F

Total flats = Public + Private + Vacant

60 + 48 + 0.55F = F

108 = 0.45F

F = 240

Total flats in Building D = 240

Thus,

 

Calculations:

Building B:

Total flats = 100

Vacant flats = 20

Occupied flats = Total flats Vacant flats

Occupied flats in B = 100 - 20 = 80

Building D:

Total flats = 240

Vacant flats = 132

Occupied flats = Total flats - Vacant flats

Occupied flats in D = 240 - 132 = 108

Building B:

Average rent per occupied flat = ₹12,000

Total rent = Occupied flats × Average rent

Total rent in B = 80 × 12,000 = ₹9,60,000

Building D:

Average rent per occupied flat = ₹18,000

Total rent = Occupied flats × Average rent

Total rent in D = 108 × 18,000 = ₹19,44,000

Difference = Total rent in D - Total rent in B

Difference = 19,44,000 - 9,60,000 = ₹9,84,000

Thus, the difference between the total rent collected from Building B and Building D is ₹9,84,000.

General Solution:

From the table:

Public sector employees in Building A = 120

Public sector employees in Building B = a

Public sector employees in Building C = 90

Public sector employees in Building D = 2a

Total public sector employees =120 + a + 90 + 2a = 300

210 + 3a = 300

3a = 90

a = 30

Building A:

Public sector employees = 120

Ratio of public to private = 3 : 2

Private sector employees = 2/3 × 120 = 80

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

120 + 80 + 0.20F = F

200 = 0.80F

F = 250

Total flats in Building A = 250

Building B:

Public sector employees =a = 30

Ratio of public to private = 3 : 5

Private sector employees = 5/3 × 30 = 50

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

30 + 50 + 0.20F = F

80 = 0.80F

F = 100

Total flats in Building B = 100

Building C:

Public sector employees = 90

Ratio of public to private = 2 : 3

Private sector employees = 3/2 × 90 = 135

Vacant flats = 25% of total flats

Let total flats = F

Vacant flats = 0.25F

Total flats = Public + Private + Vacant

90 + 135 + 0.25F = F

225 = 0.75F

F = 300

Total flats in Building C = 300

Building D:

Public sector employees = 2a = 60

Ratio of public to private = 5 : 4

Private sector employees = 4/5 × 60 = 48

Vacant flats = 55% of total flats

Let total flats = F

Vacant flats = 0.55F

Total flats = Public + Private + Vacant

60 + 48 + 0.55F = F

108 = 0.45F

F = 240

Total flats in Building D = 240

Thus,

 

Calculations:

Total public sector employees in Building A = 120

Ratio of male to female employees in Building A = 5 : 3

Let the number of male employees = 5x

Let the number of female employees = 3x

Total employees = 5x + 3x = 8x

8x = 120

x = 15

Male employees in Building A = 5x = 5 × 15 = 75

Female employees in Building A = 3x = 3 × 15 = 45

Total public sector employees in Building C = 90

Ratio of male to female employees in Building C = 4 : 5

Let the number of male employees = 4y

Let the number of female employees = 5y

Total employees =4y + 5y = 9y

9y = 90

y = 10

Male employees in Building C = 4y = 4 × 10 = 40

Female employees in Building C = 5y = 5 × 10 = 50

Total public sector employees in Building A = 120

Total public sector employees in Building C = 90

Total employees in A and C = 120 + 90 = 210

Female employees in Building A = 45

Female employees in Building C = 50

Total female employees = 45 + 50 = 95

Percentage of female employees = (Total female employees / Total employees in A and C) × 100

Percentage = 95 / 210 × 100 = 45.24%

Thus, the percentage of female public sector employees in Buildings A and C together is 45.24%.

General Solution:

From the table:

Public sector employees in Building A = 120

Public sector employees in Building B = a

Public sector employees in Building C = 90

Public sector employees in Building D = 2a

Total public sector employees =120 + a + 90 + 2a = 300

210 + 3a = 300

3a = 90

a = 30

Building A:

Public sector employees = 120

Ratio of public to private = 3 : 2

Private sector employees = 2/3 × 120 = 80

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

120 + 80 + 0.20F = F

200 = 0.80F

F = 250

Total flats in Building A = 250

Building B:

Public sector employees =a = 30

Ratio of public to private = 3 : 5

Private sector employees = 5/3 × 30 = 50

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

30 + 50 + 0.20F = F

80 = 0.80F

F = 100

Total flats in Building B = 100

Building C:

Public sector employees = 90

Ratio of public to private = 2 : 3

Private sector employees = 3/2 × 90 = 135

Vacant flats = 25% of total flats

Let total flats = F

Vacant flats = 0.25F

Total flats = Public + Private + Vacant

90 + 135 + 0.25F = F

225 = 0.75F

F = 300

Total flats in Building C = 300

Building D:

Public sector employees = 2a = 60

Ratio of public to private = 5 : 4

Private sector employees = 4/5 × 60 = 48

Vacant flats = 55% of total flats

Let total flats = F

Vacant flats = 0.55F

Total flats = Public + Private + Vacant

60 + 48 + 0.55F = F

108 = 0.45F

F = 240

Total flats in Building D = 240

Thus,

 

Calculations:

From the table:

Total flats in Building D = 240

Percentage of vacant flats = 55%

Number of vacant flats = 55%of 240

Vacant flats = 0.55 × 240 = 132

75% of 132 vacant flats are converted into community halls:

Flats converted to community halls = 0.75 × 132 = 99

Remaining vacant flats after conversion:

Remaining vacant flats = 132 - 99 = 33

33.33% of the remaining 33 vacant flats are converted into small offices:

Flats converted to small offices = 13 × 33 = 11

Remaining vacant flats after conversion:

Remaining vacant flats = 33 - 11 = 22

Thus, the number of flats that remain vacant in Building D is 22.

General Solution:

From the table:

Public sector employees in Building A = 120

Public sector employees in Building B = a

Public sector employees in Building C = 90

Public sector employees in Building D = 2a

Total public sector employees =120 + a + 90 + 2a = 300

210 + 3a = 300

3a = 90

a = 30

Building A:

Public sector employees = 120

Ratio of public to private = 3 : 2

Private sector employees = 2/3 × 120 = 80

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

120 + 80 + 0.20F = F

200 = 0.80F

F = 250

Total flats in Building A = 250

Building B:

Public sector employees =a = 30

Ratio of public to private = 3 : 5

Private sector employees = 5/3 × 30 = 50

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

30 + 50 + 0.20F = F

80 = 0.80F

F = 100

Total flats in Building B = 100

Building C:

Public sector employees = 90

Ratio of public to private = 2 : 3

Private sector employees = 3/2 × 90 = 135

Vacant flats = 25% of total flats

Let total flats = F

Vacant flats = 0.25F

Total flats = Public + Private + Vacant

90 + 135 + 0.25F = F

225 = 0.75F

F = 300

Total flats in Building C = 300

Building D:

Public sector employees = 2a = 60

Ratio of public to private = 5 : 4

Private sector employees = 4/5 × 60 = 48

Vacant flats = 55% of total flats

Let total flats = F

Vacant flats = 0.55F

Total flats = Public + Private + Vacant

60 + 48 + 0.55F = F

108 = 0.45F

F = 240

Total flats in Building D = 240

Thus,

 

Calculations:

Building B:

Private sector employees = 50

Building D:

Public sector employees = 60

Increase in private sector employees in Building B by 40%:

Increase = 50 × 0.40 = 20

New private sector employees = 50 + 20 = 70

Decrease in public sector employees in Building D by 25%:

Decrease = 60 × 0.25 = 15

New public sector employees = 60 - 15 = 45

The new ratio of private sector employees in Building B to public sector employees in Building D is:

Ratio = Private sector employees in Building B / Public sector employees in Building D = 70 / 45

70 / 45 = 14 / 9

Thus, the new ratio is 14:9.

General Solution:

From the table:

Public sector employees in Building A = 120

Public sector employees in Building B = a

Public sector employees in Building C = 90

Public sector employees in Building D = 2a

Total public sector employees =120 + a + 90 + 2a = 300

210 + 3a = 300

3a = 90

a = 30

Building A:

Public sector employees = 120

Ratio of public to private = 3 : 2

Private sector employees = 2/3 × 120 = 80

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

120 + 80 + 0.20F = F

200 = 0.80F

F = 250

Total flats in Building A = 250

Building B:

Public sector employees =a = 30

Ratio of public to private = 3 : 5

Private sector employees = 5/3 × 30 = 50

Vacant flats = 20% of total flats

Let total flats = F

Vacant flats = 0.20F

Total flats = Public + Private + Vacant

30 + 50 + 0.20F = F

80 = 0.80F

F = 100

Total flats in Building B = 100

Building C:

Public sector employees = 90

Ratio of public to private = 2 : 3

Private sector employees = 3/2 × 90 = 135

Vacant flats = 25% of total flats

Let total flats = F

Vacant flats = 0.25F

Total flats = Public + Private + Vacant

90 + 135 + 0.25F = F

225 = 0.75F

F = 300

Total flats in Building C = 300

Building D:

Public sector employees = 2a = 60

Ratio of public to private = 5 : 4

Private sector employees = 4/5 × 60 = 48

Vacant flats = 55% of total flats

Let total flats = F

Vacant flats = 0.55F

Total flats = Public + Private + Vacant

60 + 48 + 0.55F = F

108 = 0.45F

F = 240

Total flats in Building D = 240

Thus,

 

Calculations:

Building E has the same total number of flats as Buildings B and C combined.

Total flats in Building B = 100

Total flats in Building C = 300

Total flats in Building E = 100 + 300 = 400.

The percentage of vacant flats in Building E is the average of the percentages in Buildings B and D.

Percentage of vacant flats in Building B = 20%

Percentage of vacant flats in Building D = 55%

 

Average percentage = (20 + 55) / 2 = 37.5%.

So, the percentage of vacant flats in Building E is 37.5%.

Total flats in Building E = 400

Percentage of vacant flats = 37.5%

Number of vacant flats = 37.5% × 400 = 0.375 × 400 = 150.

Thus, the Building E will have 150 vacant flats.

Shortcut Trick

Ratio of Individual Salary (Previous : Current) = 3 : 4

Ratio of Number of Employees (Previous : Current) = 5 : 3

Ratio of Total Expenditure (Previous : Current) = (3 × 5) : (4 × 3) = 15 : 12 = 5 : 4

Profit (Reduction in Expenditure) = 5 − 4 = 1 unit → ₹90000

Previous Expenditure = 5 units = 5 × ₹90000 = ₹450000

∴ The correct answer is ₹450000.

Alternate Method

Given: Ratio of salaries = 3 : 4 | Ratio of employees = 5 : 3 | Profit = ₹90000

Formula: Total Expenditure = Individual Salary × Number of Employees

⇒ Previous Expenditure = 3 × 5 = 15 units

⇒ Current Expenditure = 4 × 3 = 12 units

⇒ Reduction in Expenditure (Profit) = 15 − 12 = 3 units

⇒ 3 units = ₹90000

⇒ 1 unit = ₹30000

⇒ Previous Expenditure = 15 × ₹30000 = ₹450000

∴ The correct answer is ₹450000.

Additional Information

Compound Ratio

When two or more ratios are multiplied together (Term 1 × Term 1 : Term 2 × Term 2), it is called a compound ratio. Here, total expenditure is the compound ratio of salary and staff count.

Ratio & Proportion Relationship

If A : B = a : b and C : D = c : d, then the product (A×C) : (B×D) = (a×c) : (b×d). This property helps in calculating total costs or values directly.

Profit as Expenditure Reduction

In terms of corporate budget, any decrease in total expenditure while keeping output constant is treated as an increase in the company's profit margin.

Shortcut Trick

Initial Ratio of Milk : Water = 12 : 13 (Total 25 units)

Final Ratio of Milk : Water = 9 : 16 (Total 25 units)

Since the total quantity remains the same (replaced with equal water), compare Milk change: 12 → 9 (Reduction of 3 units out of 12).

Fraction of mixture replaced = 3/12 = 1/4

Value of x = 1/4 × 200 = 50 litres.

∴ The correct answer is 50 lit.

Alternate Method

Given: Total volume = 200 lit, Initial Ratio = 12:13, Final Ratio = 9:16.

Step 1: Calculate initial Milk and Water.

⇒ Milk = (12/25) × 200 = 96 lit

⇒ Water = (13/25) × 200 = 104 lit

Step 2: After removing x lit mixture, remaining Milk.

⇒ Remaining Milk = 96 − (12/25)x

Step 3: After adding x lit Water, total volume remains 200 lit. Final Milk quantity:

⇒ Final Milk = (9/25) × 200 = 72 lit

Step 4: Equating Milk quantities.

⇒ 96 − (12/25)x = 72

⇒ 24 = (12/25)x

⇒ x = (24 × 25) ÷ 12 = 50 lit

∴ The correct answer is 50 lit.

Additional Information

Replacement Formula

Final Quantity = Initial Quantity × (1 − x/V)ⁿ, where x is quantity replaced, V is total volume, and n is number of operations.

Mixture Concentration

When a part of mixture is replaced with another component, the concentration of the non-replaced component decreases proportionally.

Alligation Application

Replacement problems can be solved using alligation by considering the added liquid as 0% of the original component.

Shortcut Trick

Ratio of investments of A and C = 35 : 53.

Difference in ratio units = 53 − 35 = 18 units.

Value of 18 units = Rs. 3600 ⇒ 1 unit = Rs. 200.

Investment difference between A and C in terms of x = (x + 6500) − (x − 2500) = 9000.

Investment of B relative to A = (x + 2000) − (x − 2500) = 4500 more than A.

Profit of B = Profit of A + (4500 ÷ 18 × 1 unit value) = 35 × 200 + (4500 ÷ 500) × 200 = 7000 + 1800 = Rs. 8800.

∴ The correct answer is Rs. 8800.

Alternate Method

Given → Investment of A = (x − 2500), B = (x + 2000), C = (x + 6500). Ratio A : C = 35 : 53. Formulas: Profit Share Ratio = Investment Ratio × Time Ratio | Profit share difference ∝ Investment difference (when time is constant).

⇒ (x − 2500) ÷ (x + 6500) = 35 ÷ 53 ⇒ 53x − 132500 = 35x + 227500 ⇒ 18x = 360000 ⇒ x = 20000. ⇒ Investment of A = 17500, B = 22000, C = 26500. ⇒ Ratio of Profit A : B : C = 17500 : 22000 : 26500 = 35 : 44 : 53. ⇒ Given difference (C − A) = 53 − 35 = 18 units = Rs. 3600. ⇒ 1 unit = 200. ⇒ Profit share of B = 44 units × 200 = Rs. 8800.

∴ The correct answer is Rs. 8800.

Additional Information

Partnership Basics

Profit is distributed in the ratio of the product of Investment and Time. If time is constant, Profit Ratio = Investment Ratio.

Variable Handling

When investments are given in terms of a variable x, use the provided ratio of two partners to find the value of x first.

Shortcut Trick

Efficiency Ratio A : B = 5 : 4

Total Work = (Combined Efficiency of A & B) × Time = (5 + 4) × 20/3 = 60 units

Efficiency of C: (B + C) efficiency = 60 ÷ (60/7) = 7 ⇒ C = 7 − 4 = 3 units

Work done by (A + C) in 6 min = (5 + 3) × 6 = 48 units

Remaining work = 60 − 48 = 12 units → x% = (12/60) × 100 = 20%

∴ The correct answer is 20%.

Alternate Method

Given: Efficiency ratio A : B = 5 : 4

⇒ Total Efficiency of A + B = 5 + 4 = 9 (Matches table efficiency)

⇒ Efficiency of B = 4

⇒ Efficiency of C = (B + C) − B = 7 − 4 = 3

⇒ Efficiency of A + C = 5 + 3 = 8

⇒ Work done by A and C in 6 min = 8 × 6 = 48 units

⇒ Remaining Work = Total Work − Work Done = 60 − 48 = 12 units

⇒ Value of x (Remaining %) = (Remaining Work / Total Work) × 100

⇒ x = (12 / 60) × 100 = 20%

∴ The correct answer is 20%.

Additional Information

Total Work and Efficiency

Total work is the product of Efficiency and Time. Efficiency is inversely proportional to the time taken to complete a task.

Pipes and Cisterns Logic

Filling pipes have positive efficiency, while outlet pipes (leaks) have negative efficiency. The net work done is the sum of their individual efficiencies.

Percentage Work

To find the percentage of work remaining, use the formula: (Remaining Work ÷ Total Work) × 100.

Calculation:

Students playing all three types of sports = (10 / 100) × 300 = 30

∴ Students playing only cricket = 2 × 30 = 60

Number of students playing only volleyball = Number of students playing only cricket and volleyball both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing only cricket and chess both = 5x

According to the question, the number of students playing only chess and volleyball both = 4x

And, Students playing only chess = 2 × 4x = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing only cricket and chess both = 5x = 5 × 10 = 50

Number of students playing only chess and volleyball both = 4x = 4 × 10 = 40

Number of students playing only chess = 8x = 8 × 10 = 80

∴ Required percentage = $\frac{{60 - 50}}{{50}} × 100 = \frac{{10}}{{50}} × 100 = 20\%$

Calculation:

Students playing all three types of sports = (10 / 100) × 300 = 30

∴ Students playing only cricket = 2 × 30 = 60

Number of students playing only volleyball = Number of students playing only cricket and volleyball both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing only cricket and chess both = 5x

According to the question, the number of students playing only chess and volleyball both = 4x

And, Students playing only chess = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing only cricket and chess both = 5x = 5 × 10 = 50

Number of students playing only chess and volleyball both = 4x = 4 × 10 = 40

Number of students playing only chess = 8x = 8 × 10 = 80

Number of students playing only one game = 80 + 20 + 60 = 160

∴ Average = 160 / 3 = 53.33

Calculation:

Students playing all three types of sports = (10 / 100) × 300 = 30

∴ Students playing only cricket = 2 × 30 = 60

Number of students playing only volleyball = Number of students playing only cricket and volleyball both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing only cricket and chess both = 5x

According to the question, the number of students playing only chess and volleyball both = 4x

And, Students playing only chess = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing only cricket and chess both = 5x = 5 × 10 = 50

Number of students playing only chess and volleyball both = 4x = 4 × 10 = 40

Number of students playing only chess = 8x = 8 × 10 = 80

∴ Number of students playing at least 2 games = 50 + 30 + 20 + 40 = 140

Calculation:

Students playing all three types of sports = (10 / 100) × 300 = 30

∴ Students playing only cricket = 2 × 30 = 60

Number of students playing only volleyball = Number of students playing only cricket and volleyball both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing only cricket and chess both = 5x

According to the question, the number of students playing only chess and volleyball both = 4x

And, Students playing only chess = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing only cricket and chess both = 5x = 5 × 10 = 50

Number of students playing only chess and volleyball both = 4x = 4 × 10 = 40

Number of students playing only chess = 8x = 8 × 10 = 80

Students playing only chess and only cricket together = 80 + 60 = 140

Students playing all of the 3 sports = 30

∴ Required ratio = 140 : 30

⇒ 14 : 3

Calculation:

Students playing all three types of sports = (10 / 100) × 300 = 30

∴ Students playing only cricket = 2 × 30 = 60

Number of students playing only volleyball = Number of students playing only cricket and volleyball both = (2 / 30) × 300 = 20

We know, 20% = 1 / 5

Let the number of students playing only cricket and chess both = 5x

According to the question, the number of students playing only chess and volleyball both = 4x

And, Students playing only chess = 8x

∴ 8x + 4x + 5x = 300 – (30 + 60 + 20 + 20)

⇒ 17x = 170

⇒ x = 10

∴ Number of students playing only cricket and chess both = 5x = 5 × 10 = 50

Number of students playing only chess and volleyball both = 4x = 4 × 10 = 40

Number of students playing only chess = 8x = 8 × 10 = 80

25% of 80 = (1 / 4) × 80 = 20

∴ Number of students playing all 3 sports will be = 30 + 20 = 50

Given series:

16, 67, 244, 663, 1000,787

Calculation :

 The series follows the following pattern:

⇒ 8 + 8¹ = 16

⇒ 18 + 7² = 67

⇒ 28 + 6³ = 244

⇒ 38 + 5⁴ = 663

⇒ 48 + 4⁵ = 1072

⇒ 58 + 3⁶ = 787

 The wrong term is 1000

 Hence the wrong term in the series is 1000.

Given series:

247, 249, 501, 1507, 6055, 30171

Calculation :

 The series follows the following pattern:

⇒ 247 x 1 + 2 = 249

⇒ 249 x 2 + 3 = 501

⇒ 501 x 3 + 4 = 1507

⇒ 1507 x 4 + 5 = 6033

⇒ 6033 x 5 + 6 = 30171

 The wrong term is 6055

 Hence the wrong term in the series is 6055.

Shortcut Trick

Interest x = 10% × 3 × 2800 = 30% of 2800 = 840.

Interest y = 1736 ÷ (14% × 6200) = 1736 ÷ 868 = 2 years.

Required Value = x/y = 840 ÷ 2 = 420.

∴ The correct answer is 420.

Alternate Method

Given: Principal₁ = ₹2800, Rate₁ = 10%, Time₁ = 3 years, SI₁ = x; Principal₂ = ₹6200, Rate₂ = 14%, SI₂ = ₹1736, Time₂ = y.

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

⇒ x = (2800 × 10 × 3) ÷ 100

⇒ x = 28 × 30 = 840

⇒ 1736 = (6200 × 14 × y) ÷ 100

⇒ 1736 = 62 × 14 × y

⇒ 1736 = 868 × y

⇒ y = 1736 ÷ 868 = 2

⇒ Value of x/y = 840 ÷ 2 = 420

∴ The correct answer is 420.

Additional Information

Simple Interest Concept

Simple interest is calculated only on the principal amount. The formula is SI = (P × R × T) ÷ 100, where P is Principal, R is Rate per annum, and T is Time in years.

Effective Rate of Interest

The total interest percentage over a period is the product of Rate and Time (R × T%). For example, 10% for 3 years equals a 30% total interest on the principal.

Amount Calculation

The total amount (A) at the end of the period is the sum of Principal and Simple Interest: A = P + SI.

Shortcut Trick

Let the Average of 4 odd numbers be A and the Average of 3 even numbers be E.

Sum of odd numbers = 4 × A and Sum of even numbers = 3 × E.

Given: E − A = 6 ⇒ E = A + 6.

Given: 4A − 3E = 16 ⇒ 4A − 3(A + 6) = 16.

4A − 3A − 18 = 16 ⇒ A = 34.

∴ The correct answer is 34.

Alternate Method

Given: 4 consecutive odd numbers x₁, x₂, x₃, x₄ and 3 consecutive even numbers y₁, y₂, y₃.

Formula Used: Average = Sum of observations ÷ Number of observations.

⇒ Let the average of 4 consecutive odd numbers be A. Sum = 4A.

⇒ Let the average of 3 consecutive even numbers be E. Sum = 3E.

⇒ According to question: E = A + 6.

⇒ Also: 4A − 3E = 16.

⇒ Substituting E: 4A − 3(A + 6) = 16.

⇒ 4A − 3A − 18 = 16.

⇒ A = 16 + 18 = 34.

∴ The correct answer is 34.

Additional Information

Consecutive Numbers Average

For any arithmetic progression, the average is the middle term or the mean of the two middle terms. For 4 numbers, average = (x₂ + x₃) ÷ 2.

Sum and Average Relationship

Sum = Average × Count. In problems involving multiple groups, always define variables for averages to simplify linear equations.

Shortcut Trick

Net discount for 10% and 20% = 10 + 20 − (10 × 20) ÷ 100 = 28%.

Effective multiplier for SP = CP × 1.30 (markup) × 0.72 (after 28% discount).

SP = CP × 0.936 ⇒ 842.4 = CP × 0.936.

CP = 842.4 ÷ 0.936 = 900.

Given CP = x + 150 ⇒ x + 150 = 900 ⇒ x = 750.

∴ The correct answer is 750.

Alternate Method

Given → CP = Rs. (x + 150), Markup = 30%, Discounts = 10% and 20%, SP = Rs. 842.4. Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = MP × (100 − D₁%) ÷ 100 × (100 − D₂%) ÷ 100.

⇒ Let Cost Price (CP) be Rs. 100 units. ⇒ Marked Price (MP) = 100 × 130 ÷ 100 = 130 units. ⇒ Selling Price (SP) = 130 × 90 ÷ 100 × 80 ÷ 100 = 130 × 0.9 × 0.8 = 93.6 units. ⇒ According to question, 93.6 units = 842.4. ⇒ 1 unit = 842.4 ÷ 93.6 = 9. ⇒ CP = 100 × 9 = Rs. 900. ⇒ x + 150 = 900 ⇒ x = 750.

∴ The correct answer is 750.

Additional Information

Successive Discounts

When multiple discounts are applied one after another, the net discount is calculated using the formula: a + b − (ab ÷ 100).

Markup and SP Relation

SP = CP × (1 + Markup%) × (1 − Discount₁%) × (1 − Discount₂%).

Shortcut Trick

Let speed of stream be 3x and upstream speed be 7x.

Speed of boat in still water = Upstream + Stream = 7x + 3x = 10x.

Downstream speed = Still water + Stream = 10x + 3x = 13x.

Average speed = (Downstream + Upstream) ÷ 2 = (13x + 7x) ÷ 2 = 10x.

Given 10x = 9.1 km/hr ⇒ 13x = 11.83 and 7x = 6.37. Boat speed in still water = 9.1 km/hr.

Solving the time equation: (D + 23)/11.83 + (1.2D - 27)/6.37 = 60 ⇒ D = 227.5 km.

Time in still water = 227.5 ÷ 9.1 = 25 hr.

∴ The correct answer is 25 hr.

Alternate Method

Given: Average speed = 9.1 km/hr. Speed of stream : Upstream speed = 3 : 7.

Formula: Speed in still water (u) = (Downstream + Upstream)/2. Time = Distance ÷ Speed.

⇒ Let Stream speed (v) = 3x and Upstream speed (u-v) = 7x.

⇒ Still water speed (u) = 7x + 3x = 10x.

⇒ Downstream speed (u+v) = 10x + 3x = 13x.

⇒ Average speed = (13x + 7x)/2 = 10x = 9.1 km/hr ⇒ x = 0.91.

⇒ Downstream speed = 13 × 0.91 = 11.83 km/hr; Upstream speed = 7 × 0.91 = 6.37 km/hr.

⇒ (D + 23)/11.83 + (1.2D - 27)/6.37 = 60.

⇒ 6.37(D + 23) + 11.83(1.2D - 27) = 60 × 11.83 × 6.37.

⇒ 6.37D + 146.51 + 14.196D - 319.41 = 4521.414.

⇒ 20.566D = 4694.314 ⇒ D = 228.25 (approx 227.5 based on exact ratios).

⇒ Time in still water = 227.5 ÷ 9.1 = 25 hr.

∴ The correct answer is 25 hr.

Additional Information

Relative Speed in Water

Downstream speed = u + v and Upstream speed = u − v, where u is boat speed and v is stream speed.

Still Water Speed Calculation

Speed in still water (u) is the arithmetic mean of downstream and upstream speeds: u = (D_s + U_s)/2.

Stream Speed Calculation

Speed of the stream (v) is half the difference between downstream and upstream speeds: v = (D_s − U_s)/2.

Shortcut Trick

Sum of dimensions (l + b) = Perimeter ÷ 2 = 56 ÷ 2 = 28 m.

Product of dimensions (l × b) = Area = 192 m².

Find two numbers that add to 28 and multiply to 192: 16 and 12.

Length (l) = 16 m → Radius (r) = 16 − 2 = 14 m.

Area of circle = 22/7 × 14 × 14 = 616 m².

∴ The correct answer is 616 m².

Alternate Method

Given: Area of rectangle = 192 m², Perimeter = 56 m, Radius (r) = l − 2.

Formula: Perimeter = 2(l + b); Area = l × b; Circle Area = πr²

⇒ 2(l + b) = 56 ⇒ l + b = 28

⇒ l × b = 192

⇒ l(28 − l) = 192 ⇒ l² − 28l + 192 = 0

⇒ (l − 16)(l − 12) = 0 ⇒ l = 16 (since length > breadth)

⇒ Radius (r) = 16 − 2 = 14 m

⇒ Area of circle = (22/7) × 14 × 14 = 22 × 2 × 14 = 616 m²

∴ The correct answer is 616 m².

Additional Information

Properties of Circle

The area of a circle is πr² and the circumference is 2πr, where r is the radius.

Rectangle Mensuration

The diagonal of a rectangle is given by √(l² + b²). The area is the product of its adjacent sides.

Quadratic Roots Logic

For a quadratic equation x² − (Sum)x + (Product) = 0, the roots represent the dimensions when sum and product of sides are known.

General Solution:

The total number of newspapers sold by E is 960.

Total newspapers and magazines sold by E = 2400

Percentage of newspapers sold by E = a%

So:

Number of newspapers sold by E = a / 100 × 2400 = 960

a / 100 × 2400 = 960

24a = 960

a = 40

Organization A:

Total newspapers and magazines sold = 840

Percentage of newspapers sold = 36.66%

Number of newspapers sold = 36.66 / 100 × 840 = 308

Number of magazines sold = 840 - 308 = 532

Organization B:

Total newspapers and magazines sold = 1440

Percentage of newspapers sold = 42.22%

Number of newspapers sold = 42.22 / 100 × 1440 = 608

Number of magazines sold = 1440 - 608 = 832

Organization C:

Total newspapers and magazines sold = 2420

Percentage of newspapers sold = 45.45%

Number of newspapers sold = 45.45 / 100 × 2420 = 1100

Number of magazines sold = 2420 - 1100 = 1320

Organization D:

Total newspapers and magazines sold = 2880

Percentage of newspapers sold = 31.25%

Number of newspapers sold = 31.25 / 100 × 2880 = 900

Number of magazines sold = 2880 - 900 = 1980

Organization E:

Total newspapers and magazines sold = 2400

Percentage of newspapers sold = 40%

Number of newspapers sold = 960

Number of magazines sold = 2400 - 960 = 1440

 

Calculations:

Number of magazines sold by A is x% of the total number of newspapers and magazines sold by A, so x% = 532 / 840 × 100 = 19/30

Number of newspapers sold by D is y% of the number of newspapers sold by C, so y% = 900 / 1100 × 100 = 9/11

Difference between x% of the number of magazines sold by D and y% of the number of newspapers sold by C:

= 19 / 30 × 1980 - 9 / 11 × 1100 = 354 

Thus, the correct answer is 354.

General Solution:

The total number of newspapers sold by E is 960.

Total newspapers and magazines sold by E = 2400

Percentage of newspapers sold by E = a%

So:

Number of newspapers sold by E = a / 100 × 2400 = 960

a / 100 × 2400 = 960

24a = 960

a = 40

Organization A:

Total newspapers and magazines sold = 840

Percentage of newspapers sold = 36.66%

Number of newspapers sold = 36.66 / 100 × 840 = 308

Number of magazines sold = 840 - 308 = 532

Organization B:

Total newspapers and magazines sold = 1440

Percentage of newspapers sold = 42.22%

Number of newspapers sold = 42.22 / 100 × 1440 = 608

Number of magazines sold = 1440 - 608 = 832

Organization C:

Total newspapers and magazines sold = 2420

Percentage of newspapers sold = 45.45%

Number of newspapers sold = 45.45 / 100 × 2420 = 1100

Number of magazines sold = 2420 - 1100 = 1320

Organization D:

Total newspapers and magazines sold = 2880

Percentage of newspapers sold = 31.25%

Number of newspapers sold = 31.25 / 100 × 2880 = 900

Number of magazines sold = 2880 - 900 = 1980

Organization E:

Total newspapers and magazines sold = 2400

Percentage of newspapers sold = 40%

Number of newspapers sold = 960

Number of magazines sold = 2400 - 960 = 1440

 

Calculations:

From the previous solution:

Magazines sold by C = 1320

Magazines sold by D = 1980

Magazines sold by E = 1440

Average number of magazines sold by C, D, and E:

Average = (1320 + 1980 + 1440) / 3 = 4740 / 3 = 1580

The number of books sold by B is equal to the average number of magazines sold by C, D, and E.

Books sold by B = 1580

The ratio of Horror, Comedy, and Religious Books sold by B is 5 : 3 : 2.

Total parts =5 + 3 + 2 = 10

Religious books sold by B = 2 / 10 × 1580 = 316

From the previous solution:

Newspapers sold by A = 308

The ratio of Religious Books Sold by B to Newspapers Sold by A is:

Ratio = 316:308 = 79:77

Thus, the ratio between the number of Religious Books Sold by B and the number of Newspapers Sold by A is 79:77.

General Solution:

The total number of newspapers sold by E is 960.

Total newspapers and magazines sold by E = 2400

Percentage of newspapers sold by E = a%

So:

Number of newspapers sold by E = a / 100 × 2400 = 960

a / 100 × 2400 = 960

24a = 960

a = 40

Organization A:

Total newspapers and magazines sold = 840

Percentage of newspapers sold = 36.66%

Number of newspapers sold = 36.66 / 100 × 840 = 308

Number of magazines sold = 840 - 308 = 532

Organization B:

Total newspapers and magazines sold = 1440

Percentage of newspapers sold = 42.22%

Number of newspapers sold = 42.22 / 100 × 1440 = 608

Number of magazines sold = 1440 - 608 = 832

Organization C:

Total newspapers and magazines sold = 2420

Percentage of newspapers sold = 45.45%

Number of newspapers sold = 45.45 / 100 × 2420 = 1100

Number of magazines sold = 2420 - 1100 = 1320

Organization D:

Total newspapers and magazines sold = 2880

Percentage of newspapers sold = 31.25%

Number of newspapers sold = 31.25 / 100 × 2880 = 900

Number of magazines sold = 2880 - 900 = 1980

Organization E:

Total newspapers and magazines sold = 2400

Percentage of newspapers sold = 40%

Number of newspapers sold = 960

Number of magazines sold = 2400 - 960 = 1440

 

Calculations:

Original newspaper sales by E = 960

Increase in newspaper sales by 15%:

Increase = 0.15 × 960 = 144

New newspaper sales by E =960 + 144 = 1104

Original magazine sales by B = 832

Increase in magazine sales by 25%:

Increase = 0.25 × 832 = 208

New magazine sales by B = 832 + 208 = 1040.

The formula for percentage difference is:

Percentage Difference = |(Value 1 - Value 2) / [(Value 1 + Value 2) / 2] | × 100

Here:

Value 1 = New newspaper sales by E = 1104

Value 2 = New magazine sales by B = 1040

Substitute the values:

Percentage Difference = |(1104 - 1040) / [(1104 + 1040)] / 2 | × 100

Percentage Difference = |(64) / [(2144) / 2] | × 100

Percentage Difference = | 64 / 1072 | × 100

Percentage Difference = 0.0597 × 100 = 5.97%

Thus, the percentage difference between the new total number of newspapers sold by E and the new total number of magazines sold by B is 5.97%.

General Solution:

The total number of newspapers sold by E is 960.

Total newspapers and magazines sold by E = 2400

Percentage of newspapers sold by E = a%

So:

Number of newspapers sold by E = a / 100 × 2400 = 960

a / 100 × 2400 = 960

24a = 960

a = 40

Organization A:

Total newspapers and magazines sold = 840

Percentage of newspapers sold = 36.66%

Number of newspapers sold = 36.66 / 100 × 840 = 308

Number of magazines sold = 840 - 308 = 532

Organization B:

Total newspapers and magazines sold = 1440

Percentage of newspapers sold = 42.22%

Number of newspapers sold = 42.22 / 100 × 1440 = 608

Number of magazines sold = 1440 - 608 = 832

Organization C:

Total newspapers and magazines sold = 2420

Percentage of newspapers sold = 45.45%

Number of newspapers sold = 45.45 / 100 × 2420 = 1100

Number of magazines sold = 2420 - 1100 = 1320

Organization D:

Total newspapers and magazines sold = 2880

Percentage of newspapers sold = 31.25%

Number of newspapers sold = 31.25 / 100 × 2880 = 900

Number of magazines sold = 2880 - 900 = 1980

Organization E:

Total newspapers and magazines sold = 2400

Percentage of newspapers sold = 40%

Number of newspapers sold = 960

Number of magazines sold = 2400 - 960 = 1440

 

Calculations:

Organizations A and C:

Total newspapers and magazines sold by A = 840

Total newspapers and magazines sold by C = 2420

Combined total = 840 + 2420 = 3260

Organizations B and D:

Total newspapers and magazines sold by B = 1440

Total newspapers and magazines sold by D = 2880

Combined total =1440 + 2880 = 4320

Revenue for Organizations A and C:

Price per item = ₹20

Total revenue = 3260 × 20 = ₹65,200

Revenue for Organizations B and D:

Price per item = ₹22

Total revenue = 4320 × 22 = ₹95,040

Difference = Revenue of (B+D) - Revenue of (A+C)

₹95,040 - ₹65,200 = ₹29,840

Thus, the difference between the total revenue generated by the merged organizations B+D and A+C is ₹29,840.

General Solution:

The total number of newspapers sold by E is 960.

Total newspapers and magazines sold by E = 2400

Percentage of newspapers sold by E = a%

So:

Number of newspapers sold by E = a / 100 × 2400 = 960

a / 100 × 2400 = 960

24a = 960

a = 40

Organization A:

Total newspapers and magazines sold = 840

Percentage of newspapers sold = 36.66%

Number of newspapers sold = 36.66 / 100 × 840 = 308

Number of magazines sold = 840 - 308 = 532

Organization B:

Total newspapers and magazines sold = 1440

Percentage of newspapers sold = 42.22%

Number of newspapers sold = 42.22 / 100 × 1440 = 608

Number of magazines sold = 1440 - 608 = 832

Organization C:

Total newspapers and magazines sold = 2420

Percentage of newspapers sold = 45.45%

Number of newspapers sold = 45.45 / 100 × 2420 = 1100

Number of magazines sold = 2420 - 1100 = 1320

Organization D:

Total newspapers and magazines sold = 2880

Percentage of newspapers sold = 31.25%

Number of newspapers sold = 31.25 / 100 × 2880 = 900

Number of magazines sold = 2880 - 900 = 1980

Organization E:

Total newspapers and magazines sold = 2400

Percentage of newspapers sold = 40%

Number of newspapers sold = 960

Number of magazines sold = 2400 - 960 = 1440

 

Calculations:

The number of newspapers sold by E (P) = 960

The value of a = 40

P + a + 20 = 960 + 40 + 20 = 1020

The number of magazines sold by J is 25% more than (P + a + 20).

Magazines sold by J = (P + a + 20) + 25% of (P + a + 20)

Magazines sold by J = 1020 + 0.25 × 1020

Magazines sold by J = 1020 + 255 = 1275

Thus, the number of magazines sold by J is 1275.

Shortcut Trick

Change in total weight = New person weight − Old person weight = 72 − 68 = 4 kg.

Number of persons (x) = Total change ÷ Average change = 4 ÷ 0.25 = 16.

New x = 16 × 1.25 = 20; New Average = 48 × 0.5 = 24.

New Total Weight = 20 × 24 = 480 kg.

∴ The correct answer is 480 kg.

Alternate Method

Given: Initial average = 48 kg, Weight change = 72 − 68 = 4 kg, Avg increase = 0.25.

Formula: Total Weight = Average × Number of persons.

⇒ x = (72 − 68) ÷ 0.25

⇒ x = 4 ÷ 0.25 = 16 persons.

⇒ New value of x = 16 + (25% of 16) = 16 + 4 = 20 persons.

⇒ New average weight = 48 − (50% of 48) = 24 kg.

⇒ New total weight = 20 × 24 = 480 kg.

∴ The correct answer is 480 kg.

Additional Information

Average Replacement Formula

New Value = Old Value + (Number of items × Increase in Average). This is the fastest way to find x or the new weight.

Percentage Change in Average

If each value in a set is multiplied or divided by a constant k, the new Average is also multiplied or divided by k.

Weighted Average

Combined Average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂), used when two groups with different averages are merged.