SBI PO Prelims Memory Based Paper (Held On: 16 March 2025 Shift 1) (Previous Year Paper)

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 (1):

The overwhelming (1) of putting on layers of clothing that hinder free movement, the absence of sunshine that slows down my mental processes, cold extremities and the widespread lethargy in people around me, all contribute to my (2) with winter.

• This sentence describes negative aspects associated with winter, such as putting on layers of clothing, lack of sunshine, and lethargy.
• Blank (1) should be filled with a word indicating a negative emotion or experience.
• Now, let's understand the meanings of the given words as options:
• Serenity - the state of being calm, peaceful, and untroubled (शांति)
• For Example -
• Amidst the chaos, she found solace in the gentle embrace of nature, embracing serenity.
• Excitement - the state of being emotionally aroused and eager (उत्साह)
• For Example -
• The children's excitement was palpable as they waited for the amusement park rides to start.
• Frustration - the feeling of being upset or annoyed, especially because of the inability to change or achieve something (आकुलता)
• For Example -
• The constant technical glitches in the software led to frustration among the users.
• Dexterity - skill in performing tasks, especially with the hands (कुशलता)
• For Example -
• The juggler's dexterity amazed the audience as he flawlessly tossed and caught the objects in the air.
• Satisfaction - the fulfilment of one's wishes, expectations, or needs, or the pleasure derived from this (तृप्ति)
• For Example -
• Completing the project ahead of schedule gave the team a sense of satisfaction and accomplishment.
• So, given the context of the sentence and the negative aspects associated with winter, the most appropriate option to fill in the blank labelled as (1) is "frustration." It aligns with the idea that the overwhelming frustration of dealing with layers of clothing, lack of sunshine, and lethargy contributes to the speaker's dislike of winter.
• Therefore, the correct answer is "frustration."
• The complete sentence would be: "The overwhelming frustration of putting on layers of clothing that hinder free movement, the absence of sunshine that slows down my mental processes, cold extremities and the widespread lethargy in people around me, all contribute to my (2) with winter."

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 (2):

The overwhelming (1) of putting on layers of clothing that hinder free movement, the absence of sunshine that slows down my mental processes, cold extremities and the widespread lethargy in people around me, all contribute to my (2) with winter.

• This sentence describes the challenges and negative aspects associated with winter, such as the difficulty of wearing layers of clothing, lack of sunshine affecting mental processes, and overall discomfort.
• Blank (2) should be filled with a word indicating a negative sentiment of complaint or protest.
• Now, let's understand the meanings of the given words as options:
• Nostalgia - a sentimental longing or wistful affection for the past, typically for a period or place with happy personal associations (वात्सल्य)
• For Example -
• Flipping through the old photo album filled her with nostalgia for the carefree days of her childhood.
• Audacity - the willingness to take bold risks; rude or disrespectful behavior; impudence (ढिठाई)
• For Example -
• His audacity in challenging the established norms of the industry led to both admiration and criticism.
• Indifference - lack of interest, concern, or sympathy; unimportance (उदासीनता)
• For Example -
• The manager's indifference to the team's concerns created a sense of frustration among the employees.
• Enthusiasm - intense and eager enjoyment, interest, or approval (उत्साह)
• For Example -
• The students' enthusiasm for the science experiment was evident as they eagerly participated in the hands-on activity.
• Grievance - a real or imagined cause for complaint or protest, typically unfair treatment (शिकायत)
• For Example -
• Addressing the employees' grievances became a priority for the HR department to maintain a positive work environment.
• So, given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (2) is "grievance." It aligns with the idea that the challenges and discomfort associated with winter contribute to the speaker's complaint or protest against the season.
• Therefore, the correct answer is "grievance."
• The complete sentence would be: "The overwhelming frustration of putting on layers of clothing that hinder free movement, the absence of sunshine that slows down my mental processes, cold extremities and the widespread lethargy in people around me, all contribute to my grievance with winter."

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):

One of the primary reasons people seem to cherish winter is the feeling of (3) it brings.

• This sentence discusses one of the reasons people enjoy winter.
• Blank (3) should be filled with a word describing the positive feeling associated with the season.
• Now, let's understand the meanings of the given words as options:
• Obscurity - the state of being unknown, inconspicuous, or not easily understood (अस्पष्टता)
• For Example -
• The artist's early works remained in obscurity until a retrospective exhibition brought them into the spotlight.
• Cosiness - a feeling of warmth, comfort, and intimacy (आरामदाइकी)
• For Example -
• The fireplace and soft blankets added a sense of cosiness to the living room on a cold winter evening.
• Rigidity - the quality of being stiff, inflexible, or resistant to change (कड़ापन)
• For Example -
• The rigidity of the company's old policies hindered innovation and adaptation to market trends.
• Agitation - a state of nervousness, restlessness, or excitement, often accompanied by heightened emotion (उत्तेजना)
• For Example -
• The political rally caused widespread agitation among the citizens, expressing their discontent.
• Diligence - careful and persistent effort or work (मेहनतीपन)
• For Example -
• The success of the project was attributed to the team's diligence in researching and addressing every detail.
• So, given the context and the desire for a positive feeling associated with winter, the most appropriate option to fill in the blank labelled as (3) is "cosiness." It aligns with the idea that people cherish winter for the feeling of warmth, comfort, and relaxation it brings.
• Therefore, the correct answer is "cosiness."
• The complete sentence would be: "One of the primary reasons people seem to cherish winter is the feeling of cosiness it brings."

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 (4):

This embrace of stillness and comfort during the colder months can be linked to a psychological phenomenon known as “hygge”, a Danish concept that encompasses a feeling of cosiness, contentment and (4).

• This sentence discusses the psychological phenomenon of "hygge," which is associated with feelings of cosiness and contentment during winter.
• Blank (4) should be filled with a word conveying the sense of calmness and contentment associated with "hygge."
• Now, let's understand the meanings of the given words as options:
• Revolution - a fundamental change in the way of thinking or behaving; a drastic and far-reaching change in a particular area or activity (क्रांति)
• For Example -
• The technological revolution in the past decade has transformed the way we communicate and access information.
• Exuberance - the quality of being full of energy, excitement, and cheerfulness; the state of being extremely joyful and lively (उत्साह)
• For Example -
• The children's exuberance during the holiday festivities filled the air with infectious joy.
• Agitation - a state of nervousness, restlessness, or excitement; the act of stirring or disturbing something, especially a liquid (उत्तेजना)
• For Example -
• The political rally led to increased agitation among the citizens, demanding change.
• Tranquillity - the quality or state of being calm, peaceful, and free from disturbance; a state of quiet and serenity (शांति)
• For Example -
• The serene lake surrounded by mountains provided a sense of tranquillity that attracted tourists seeking peace.
• Ambiguity - the quality of being open to more than one interpretation; uncertainty or inexactness of meaning (अस्पष्टता)
• For Example -
• The novel's ending left readers in suspense, shrouded in ambiguity and unanswered questions.
• So, given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (4) is "tranquillity." It aligns with the idea that "hygge" is associated with a feeling of calmness and contentment during the colder months.
• Therefore, the correct answer is "tranquillity."
• The complete sentence would be: "This embrace of stillness and comfort during the colder months can be linked to a psychological phenomenon known as “hygge”, a Danish concept that encompasses a feeling of cosiness, contentment and tranquillity."

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 (5):

While I find myself mentally slowing down and emotionally confused, others may find decreased light as an (5) to relax and calm them.

• This sentence discusses how some individuals may perceive the decreased light in winter as something that provides them with a chance to relax and calm down.
• Blank (5) should be filled with a word conveying a positive aspect, as the sentence suggests that some people see the decreased light as something positive.
• Now, let's understand the meanings of the given words as options:
• Opportunity - a favourable or advantageous circumstance or combination of circumstances that can lead to progress or success (अवसर)
• For Example -
• The internship provided her with the perfect opportunity to gain valuable work experience in her field.
• Hindrance - a thing that provides resistance, delay, or obstruction to something or someone's progress or achievement (बाधा)
• For Example -
• Lack of funding proved to be a significant hindrance to the completion of the research project.
• Obstacle - a barrier, impediment, or something that obstructs or hinders progress or movement (अवरोध)
• For Example -
• Overcoming language barriers was a major obstacle for the team working on the international project.
• Isolation - the state of being separated or secluded from others; loneliness or lack of contact with others (अलगाव)
• For Example -
• The hermit chose a life of isolation in the mountains, away from the hustle and bustle of society.
• Ambiguity - the quality of being open to more than one interpretation; uncertainty or inexactness (अस्पष्टता)
• For Example -
• The novel's ending left readers in suspense, shrouded in ambiguity and unanswered questions.
• So, given the context and the meanings of the words, the most appropriate option to fill in the blank labelled as (5) is "opportunity." It aligns with the idea that some individuals view the decreased light in winter as a chance or opportunity to relax and calm themselves.
• Therefore, the correct answer is "opportunity."
• The complete sentence would be: "While I find myself mentally slowing down and emotionally confused, others may find decreased light as an opportunity to relax and calm them."

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):

The (6) fondness for the winter’s pause may be deeply rooted in the need for comfort, relaxation, and psychological healing.

• This sentence discusses the fondness for winter's pause and suggests that this fondness might be deeply rooted in the need for comfort, relaxation, and psychological healing during the winter season.
• Blank (6) should be filled with a word describing the widespread or common nature of this fondness.
• Now, let's understand the meanings of the given words as options:
• Exceptional - surpassing what is common or usual; extraordinary (असाधारण)
• For Example -
• Her exceptional talent in music earned her a scholarship to the prestigious conservatory.
• Widespread - existing or happening over a large area or among many people; common (व्यापक)
• For Example -
• The widespread use of smartphones has transformed the way we communicate and access information.
• Irrelevant - not connected with or relevant to something; not applicable (अनुपयुक्त)
• For Example -
• His comments were completely irrelevant to the topic being discussed, confusing the meeting.
• Scattered - dispersed or spread over a wide area; not concentrated (विच्छिन्न)
• For Example -
• The scattered leaves on the ground indicated the onset of autumn.
• Transient - lasting only for a short time; temporary (क्षणिक)
• For Example -
• The joy of winning the lottery was transient, as the winner soon faced new challenges and responsibilities.
• So, given the context, the most appropriate option to fill in the blank labelled as (6) is "widespread." It aligns with the idea that the fondness for winter's pause is prevalent, suggesting that many people experience it.
• Therefore, the correct answer is "widespread."
• The complete sentence would be: "The widespread fondness for the winter’s pause may be deeply rooted in the need for comfort, relaxation, and psychological healing."

The correct answer is Option 2.

Key Points

• Part (C) of the sentence i.e. "whereas talking to her" is erroneous.
• 'Whereas' is used in cases where two events contradict each other. (जबकि (ऐसी स्थिति दर्शाने के लिए प्रयुक्त जो भिन्‍न है))
• Example: He eats meat, whereas she’s a vegetarian.
• "While" means during the time that; when. (उस समय जब; जब)
• Example: He always phones while we’re having lunch.
• It should be replaced with 'while' which refers to a situation where two events occur simultaneously, as is the case here (assignment completion and talking over the phone).
• One more error is in the usage of "her."
• As the sentence is referring to a masculine pronoun "he", so "his" must be used before "friend."
• Hence, option 2 is the correct answer.
• The correct answer would be: "Yesterday, he was completing his assignment while talking to his friend over the phone."​

The correct answer is Option 4.

Key Points  

• Part (D) of the sentence i.e. "believes they ended in victory" is erroneous.
• "Believing" means to think that something is true, correct, or real. (विश्‍वास करना, सही मान लेना)
• "Believing" is a participle that adds an independent sentence - they ended in victory - to the preceding independent sentence.
• "Believing" is used to indicate the Prime Minister's current belief about the past events.
• Hence, option 4 is the correct answer.
• The correct answer would be: "Pakistan is re-enacting battles that the Prime Minister has fought once before, believing they ended in victory."​

The correct answer is Option 2.

Key Points 

• Part (B) of the sentence i.e. "midst the pandemic" is erroneous.
• The equivalent prepositions are amidst and in the midst of.
• Amidst: in the middle of; amid. (के बीच में; के बीच)
• Midst: the middle of something; among a group of people or things. (किसी वस्‍तु का मध्य; लोगों या वस्‍तुओं के बीच)
• Hence, option 2 is the correct answer.
• The correct answer would be:
• The following year, in the midst of the pandemic, the Tate transformed the prize into a series of bursaries.
• OR
• The following year, amidst the pandemic, the Tate transformed the prize into a series of bursaries.

The correct answer is Option 5.

Key Points    

• The given sentence is grammatically correct and free from errors.
• Even though the singular form Greater number is the correct usage, in the context of this sentence, it infers great number of people from each country and hence the term numbers is used to define people from different countries.
• There doesn't appear to be any mistake in the sentence.
• Hence, option 5 is the correct answer.

The correct answer is Option 3.

 

Key Points

• The passage mentions that Arjun's workshop is situated near the riverbank.
• It is emphasized in the context that his creative workspace is close to the Mandovi River.
• The proximity to the river provides him with the resources needed for his art.

Therefore, the correct answer is Option 3: Near the riverbank.

 

Relevant Text from Passage: "His workshop, situated near the riverbank, was a hub of creativity where he transformed simple clay into magnificent works of art."

 

Additional Information

• Option 1: "In the village center," would imply a central location within the village, not near the river.
• Option 2: "On a hilltop," suggests an elevated location which is not mentioned in the passage.
• Option 4: "In Margao," refers to a neighbouring town, incorrect as the workshop is in Manikpur.
• Option 5: "Inside a hidden cave," relates to the location where the Moonlit Clay was found, not the workshop.

The correct answer is Option 2.

 

Key Points

• The passage mentions that the elderly visitor who brought Arjun the ancient manuscript is named Ravi.
• Ravi is described as an elderly man from the neighbouring town of Margao.
• He presented Arjun with a beautifully wrapped package containing the manuscript titled "The Secrets of the Sacred Clay."

Therefore, the correct answer is Option 2: Ravi.

 

Relevant Text from Passage: "One sunny morning, Arjun received a visitor from the neighbouring town of Margao. The visitor, an elderly man named Ravi, handed Arjun a beautifully wrapped package tied with a saffron ribbon."

 

Additional Information

• Option 1: "Raju," does not match the name mentioned in the passage.
• Option 3: "Rajesh," is incorrect as the visitor's name is Ravi.
• Option 4: "Rohit," is also incorrect as the visitor's name is stated as Ravi.
• Option 5: "Ramesh," is not mentioned in the passage either.

The correct answer is Option 3.

 

Key Points

• The passage describes Moonlit Clay as having the unique property of infusing artistic creations with life-like qualities and unmatched beauty.
• This property is what makes it rare and sought after by Arjun.
• Such characteristics help Arjun to create works that seem incredibly detailed and realistic.

Therefore, the correct answer is Option 3: It can infuse artistic creations with life-like qualities and unmatched beauty.

 

Relevant Text from Passage: "As Arjun meticulously studied the manuscript, he discovered a mention of a rare type of clay known as the 'Moonlit Clay.' It was said to be found only in a hidden cave on the full moon night and possessed the power to infuse artistic creations with life-like qualities and unmatched beauty."

 

Additional Information

• Option 1: "It is easy to mold into shapes," is not mentioned as a unique property of the Moonlit Clay.
• Option 2: "It changes color in sunlight," is not described in the context of the Moonlit Clay's properties.
• Option 4: "It is heavier than ordinary clay," is not stated in the passage.
• Option 5: "It cannot be fired in a kiln," is not the unique property mentioned in the passage.

The correct answer is Option 3.

 

Key Points

• Statement A: Arjun's work attracted visitors from all over India.
• This statement is incorrect as the passage only mentions visitors from Goa and beyond, not all over India.
• Statement B: Ravi handed Arjun a beautifully wrapped package tied with a red ribbon.
• This statement is incorrect as the passage specifies that the package was tied with a saffron ribbon.
• Statement C: Arjun taught the villagers the art of pottery and the importance of preserving natural resources.
• This statement is correct as it accurately reflects the context provided in the passage.

Therefore, the correct answer is: Only C.

The correct answer is 'gleaming'.

 

Key Points

• The word "gleaming" means shining brightly, especially with reflected light.
• In the context of the sentence, the phrase "silvery clay, gleaming in the moonlight" fits well as it describes the clay glowing or shining in the moonlight.
• The other options: "hidden," "sparkling," "submerged," and "drying" do not fit the context appropriately.

​Therefore, the correct answer is 'Option 1'.

Complete Sentence: There, he discovered a deposit of silvery clay, gleaming in the moonlight.

Additional Information

• Hidden (छुपा हुआ): means concealed or not visible.
• Sparkling (चमकदार): means shining with bright flashes of light, usually used for something that glitters more dynamically.
• Submerged (डूबा हुआ): means under the surface of water or another liquid.
• Drying (सूख रहा): means becoming dry.

The correct answer is: Option 3, i.e., “Majestic”.

Key Points

• The word "magnificent" means something that is splendid or impressive in appearance, size, or quality. (शानदार)
• Example: The palace was a magnificent example of Baroque architecture.
• The word "majestic" refers to something that has grandeur or beauty, evoking admiration and respect. (राजसी)
• Example: The majestic mountains stood tall and proud against the horizon.
• Hence, we can infer that the word 'majestic' is similar in meaning to 'magnificent'.

Therefore, the correct answer is: Majestic.

Additional Information

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

• Ordinary (साधारण): Something that is common or not special.
• Example: She wore an ordinary dress to the market.
• Ugly (बदसूरत): Something that is unpleasant to look at; unattractive.
• Example: The old building looked ugly with its crumbling walls.
• Simple (सरल): Something that is easily understood or not complicated.
• Example: He gave a simple explanation of the process.
• Modest (विनम्र): Having or showing a moderate estimation of one’s abilities; not boastful.
• Example: Despite his success, he remained modest and humble.

The correct answer is: Option 2, i.e., “Isolated”.

Key Points

• The word "secluded" means something that is not seen or visited by many people; sheltered and private. (एकांत)
• Example: They found a secluded beach where they could relax without any disturbance.
• The word "isolated" refers to something that is far away from other places, buildings, or people; remote. (अलग-थलग)
• Example: The cabin was in an isolated part of the forest, far from any other homes.
• Hence, we can infer that the word 'isolated' is similar in meaning to 'secluded'.

Therefore, the correct answer is: Isolated.

Additional Information

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

• Enclosed (संलग्न): Something that is surrounded or closed off on all sides.
• Example: The garden was enclosed by a high wall.
• Busy (व्यस्त): Engaged in activity; having a lot to do.
• Example: The market was very busy with people doing their shopping.
• Discovered (खोज लिया): Found out something that was not known before.
• Example: They discovered a hidden treasure in the old house.
• Serene (शांत): Calm, peaceful, and untroubled.
• Example: The lake was serene and still in the early morning light.

The correct answer is: Option 1 i.e., “Meanly”.

Key Points

• The word "generously" means in a way that shows a readiness to give more of something, especially money, than is strictly necessary or expected. (उदारतापूर्वक)
• Example: She donated generously to the charity, helping many families in need.
• The word "meanly" refers to acting in a way that is ungenerous, unkind, or miserly. (कृपणता से)
• Example: He treated his employees meanly, rarely giving them proper recognition or rewards.
• Hence, we can infer that the opposite of 'generously' is 'meanly'.

Therefore, the correct answer is: Meanly.

Additional Information

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

• Lavishly (खूब खर्च करने के तरीके से): In a rich, elaborate, or luxurious manner.
• Example: The party was lavishly decorated with flowers and lights.
• Kindly (दयापूर्वक): In a kind manner; with kindness.
• Example: She spoke kindly to the children, offering them comfort and reassurance.
• Warmly (गर्मजोशी से): In a warm, affectionate, or friendly manner.
• Example: He greeted me warmly, making me feel instantly at ease.
• Graciously (सद्भावना से): In a courteous, kind, and pleasant manner.
• Example: She graciously accepted the award, thanking everyone for their support.

The Correct answer is: Option 5

 Key Points

To answer this question, first, let's look at the given phrases in the table:

• A. Despite the cold weather,
  

This phrase highlights a condition related to the weather.

• B. He was sure he locked the door,
  

This phrase indicates a belief that the door was locked.

• C. She didn't like the food;
  

This phrase indicates a dislike for the food.

• D. he chose the chef he wanted in his restaurant.
  

This phrase describes a decision about a chef.

• E. he didn't enjoy the film.
  

This phrase indicates a lack of enjoyment of the film.

• F. he distinctly remembered hearing the click of the latch as he turned the key.
  

This phrase describes a clear recollection of locking the door.

Now, let's understand the meanings of the given connectors in the question:

• i. since
  

It means "because" or "for the reason that."

For Example: He stayed inside since it was raining.

• ii. even though
  

It means "despite the fact that" or "although."

For Example: She went for a walk even though it was raining.

• iii. moreover
  

It means "in addition to" or "furthermore."

For Example: The project is behind schedule; moreover, it is over budget.

So, after understanding the given phrases and the connectors, we can conclude that only the combination B-i-F can make a grammatically and contextually meaningful sentence.

The complete coherent sentence would be: "He was sure he locked the door, since he distinctly remembered hearing the click of the latch as he turned the key."

The sentence logically explains why he was sure he locked the door by providing evidence of his clear memory of the event.

Therefore, the correct answer is "B-i-F."

The correct answer is option 1.

Key Points 

To answer this question, first, let's look at the given phrases in the table:

• A. The company saw an increase,
  

This phrase indicates that the company experienced growth or success.

• B. The team prepared well for the match;
  

This phrase states that the team put in effort to get ready for the game.

• C. He couldn't remember the details,
  

This phrase indicates that he forgot the specifics.

• D. the challenging economic conditions that affected many of its competitors.
  

This phrase describes the difficult financial environment that impacted other companies.

• E. she was certain he had attended the meeting.
  

This phrase expresses her confidence that he was present at the meeting.

• F. their efforts were not sufficient.
  

This phrase indicates that their attempts were inadequate.

Now, let's understand the meanings of the given connectors in the question:

• i. although
  

It means "in spite of the fact that" and is used to introduce a contrast.

For Example: Although it was raining, we went for a walk.

• ii. despite
  

It means "in spite of" and is used to show contrast.

For Example: Despite the rain, we went for a walk.

• iii. whereby
  

It means "by which" and is used to show the means or method.

For Example: They created a system whereby they could monitor progress.

So, after understanding the given phrases and the connectors, we can conclude that only the combination A-ii-D can make a grammatically and contextually coherent sentence.

The complete coherent sentence would be: "The company saw an increase, despite the challenging economic conditions that affected many of its competitors."

This sentence indicates that the company experienced growth even though other companies were negatively impacted by difficult economic conditions.

Therefore, the correct answer is A-ii-D.

The correct answer is option 2.

Key Points

Given phrases:

• A. The city council approves the new development plan,
• B. It was raining heavily,
• C. The teacher emphasized the importance of practice;
• D. the students showed remarkable improvement in their performance.
• E. the residents had mixed opinions about its impact.
• F. they continued the outdoor event, enjoying every moment.

Given connectors:

• i. because
• ii. nevertheless
• iii. so

Choices:

• 1. A-i-E
• 2. B-ii-F
• 3. C-i-D
• 4. B-iii-E
• 5. B-i-D

Explanation:

Now, let's understand the meanings of the given connectors in the question:

• i. because
  

It means "for the reason that."

For Example: She went to bed early because she was tired.

• ii. nevertheless
  

It means "in spite of that."

For Example: It was raining heavily; nevertheless, they continued the outdoor event.

• iii. so
  

It means "as a result; therefore."

For Example: He studied hard, so he passed the exam.

After understanding the given phrases and the connectors, we can conclude that only the combination B-ii-F can make a grammatically and contextually meaningful sentence.

The complete coherent sentence would be: "It was raining heavily; nevertheless, they continued the outdoor event, enjoying every moment."

The sentence describes a situation where, despite the rain, the event continued and was enjoyed.

Therefore, the correct answer is "B-ii-F."

The correct answer is option 3.

Key Points

Explanation:

• The sentence reads: "Biosecurity is no longer (A) optional because modern pandemics demonstrate (B) how biological peace (C) can destabilize economies, healthcare systems, and global threats (D)."
• Here, the word "peace" (C) doesn't fit contextually in the sentence. It needs to be swapped with "threats" (D) to make the sentence meaningful.
• After interchanging C and D, the corrected sentence becomes: "Biosecurity is no longer optional because modern pandemics demonstrate how biological threats can destabilize economies, healthcare systems, and global peace."

Therefore, the correct answer is option 3: C-D.

The correct answer is option 4.

Key Points

To make the sentence grammatically correct and meaningful, the words marked A and D need to be interchanged.

• Currently, the sentence reads: "Scientific destruction (A) should serve humanity (B) ethically, ensuring innovation enhances human (C) welfare rather than creating tools of advancement (D) or widening inequality."
• However, "Scientific destruction" and "tools of advancement" are misplaced. Interchanging A and D corrects the sentence.

After the interchange, the sentence becomes:

"Scientific advancement (A) should serve humanity (B) ethically, ensuring innovation enhances human (C) welfare rather than creating tools of destruction (D) or widening inequality."

This version is both grammatically correct and meaningful.

The correct answer is option 3.

Key Points

The pairs of words (A-B and C-D) need to be interchanged to make the sentence grammatically correct and meaningful.

• Original sentence: Digital privacy has become data (A) in the modern world as personal crucial (B) misuse governance (C) individual freedom, security, and trust in digital threatens (D).
• Step 1: Analyze the words in bold.
• Step 2: After interchanging A-B and C-D, the sentence becomes: Digital privacy has become crucial (B) in the modern world as personal data (A) misuse threatens (D) individual freedom, security, and trust in digital governance (C).
• Step 3: The corrected sentence is now grammatically correct and meaningful.
• Therefore, the correct answer is Option 3.

The correct answer is option 2.

Key Points

Explanation:

• The given sentence is: Climate change demands global damage (A), as environmental responsibility (B) transcends borders and requires (C) collective action, climate justice, and shared (D) technological solutions.
• In the given sentence, the word ‘damage’ (A) does not fit the context of the sentence. The correct word should be ‘responsibility’ (B).
• By interchanging A-B, the sentence becomes: Climate change demands global responsibility(B), as environmental damage(A) transcends borders and requires collective action, climate justice, and shared technological solutions.
• This corrected sentence is now both grammatically correct and meaningful.

Therefore, the correct answer is option 2 (A-B).

Additional Information

• Responsibility: The state or fact of being accountable or to blame for something (जिम्मेदारी).
• Damage: Physical harm caused to something (नुकसान).
• Technological: Relating to or using technology (तकनीकी).

The correct answer is 'Defiant.'

Key Points

• The first sentence talks about a prisoner who refused to go back into the cell.
• The use of the word ''refused'' in the first sentence indicates the use of the word 'defiant' in the blank.
• The second sentence talks about a child who showed an uncontrolled outburst of anger and frustration when it was time to go to bed.
• The use of the word ''tantrum'' in the second sentence indicates the use of the word 'defiant' in the blank.
• Therefore, the most appropriate word to be filled in the blank is, 'Defiant'.
• The word 'Defiant' means Showing an open refusal to obey somebody or something. (खुल्‍लम-खुल्‍ला अवज्ञा करने वाला)
  

Hence, the correct answer is option 3.

Sentence 1: The prisoner was defiant and refused to go back into his cell.

Sentence 2: The defiant child threw a tantrum when it was time to go to bed.

Additional Information

• Let us explore  the other options:
• Ancient means Belonging to a period of history that is thousands of years in the past. (प्राचीन, पुरातन, हज़ारों वर्ष पुराना)
• Compliant means Working or done in agreement with particular rules, orders, etc. (नियम, आदेश आदि के अनुसार, के अनुरूप)
• Invigilate means To watch the people taking an exam to make sure that nobody is cheating. (परीक्षा में परीक्षार्थियों पर निगाह रखना, परीक्षा में निरीक्षण-कार्य करना)
• Curious means Wanting to know or learn something. (कुछ जानने या सीखने का इच्‍छुक; उत्‍सुक, जिज्ञासु)

The correct answer is 'Survive.'

Key Points

• The first sentence talks about a man who was able to live in the snow because he had warm clothing.
• The use of the word ''able'' in the first sentence indicates the use of the word 'survive' in the blank.
• The second sentence talks about a cockroach that can sustain the radiation of a nuclear blast.
• The use of the word ''radiation'' in the second sentence indicates the use of the word 'survive' in the blank.
• Therefore, the most appropriate word to be filled in the blank is, 'Survive'.
• The word 'Survive' means To continue to live or exist in or after a difficult or dangerous situation. (कठिन या संकटपूर्ण स्थिति में या उसके बाद जीवित या अस्तित्‍व में बने रहना)
  

Hence, the correct answer is option 4.

Sentence 1: The man was able to survive in the snow because he had warm clothing.

Sentence 2: A cockroach can survive the radiation of a nuclear blast.

Additional Information

• Let us explore  the other options:
• Perception means The ability to notice or understand something. (इंद्रियों द्वारा ग्रहण या बोध; प्रत्‍यक्षण)
• Admire means To respect or like somebody/something very much. (किसी के प्रति आदर व प्रशंसा का भाव रखना)
• Assure means To make something sure or certain. (निश्‍चित करना, सुनिश्‍चित करना)
• Prospective means Likely to be or to happen; possible. (संभावित; संभव)

The correct answer is 'Cope'.

 

Key Points

• The word "cope" means to deal effectively with something difficult. (सामना करना या सामंजस्य बिठाना)
• It is often followed by the preposition "with".
• In the first sentence, it refers to managing the demands of a job and parenting. In the second sentence, it refers to dealing with harsh weather conditions.
• The other options do not fit the grammatical structure "_______ with" in this context or do not make sense.

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

Complete Sentences: 

1. The single mother could not cope with a full-time job and parenting, so she hired a nanny.
2. The farmers were unable to cope with the harsh dry weather and many of their crops died.

​

Additional Information

• Scope (क्षेत्र/विस्तार): The extent of the area or subject matter that something deals with or to which it is relevant.
• Hope (आशा): A feeling of expectation and desire for a certain thing to happen.
• Detach (अलग करना): To disconnect or separate something from something else.
• Desire (इच्छा): A strong feeling of wanting to have something or wishing for something to happen.

The correct answer is apology for using profanity.

Key Points

The meaning of the phrase ‘Pardon my French' is 'to apologize for swearing'.

'A' and 'B' don't express the correct meaning of the phrase.

'C' is the correct meaning of the phrase as used in the sentence.

Additional Information

Origin of the idiom: In the 19^th century, when English people used French expressions in conversation they often apologized for it – presumably because many of their listeners (then as now) wouldn't be familiar with the language". The phrase is uttered in an attempt to excuse the user of profanity, swearing, or curses in the presence of those offended by it, under the pretense of the words being part of a foreign language.

Usage of swearing in the English Language: When you use swear words, they allow you to convey an emotion that would otherwise not be as easy to communicate. Swear words increase your vocabulary and give you a wider range of emotions to invoke than if you didn't use any.

The correct answer is gossip idly.

Key Points

The meaning of the phrase ‘chew the fat' is 'to chat in a leisurely and prolonged way'.

'A' and 'B' don't express the correct meaning of the phrase as used in the sentence.

'C' is the correct meaning of the phrase used in the sentence.

Additional Information

Origin of the idiom: Some sources attribute the phrase "chew the fat" to sailors, who during a period of resting and conversing, or while working together, would chew on salt-hardened fat.

The correct answer is ignored and ostracized.

Key Points

The meaning of the phrase **‘**sent to Coventry' is to ostracize; to ignore or refuse to communicate with one, typically as a form of punishment. Typically, this is done by not talking to them, avoiding their company, and acting as if they no longer exist. Victims are treated as though they are completely invisible and inaudible.

'A' doesn't express the correct meaning of the phrase as used in the sentence.

'B' and 'C' are the correct meanings of the phrase as used in the sentence.

Additional Information

Origin of the idiom: The origin of this idiom is based upon 'The History of the Rebellion and Civil Wars in England', by Edward Hyde, 1st Earl of Clarendon. In this work, Clarendon recounts how Royalist troops that were captured in Birmingham were taken as prisoners to Coventry, which was a Parliamentarian stronghold. These troops were often not received warmly by the locals.

The correct answer is 'Option 4'.

Key Points

• The most appropriate option to substitute the underlined segment in the given sentence is 'frequently goes'.
• "Frequently" is the adverb that correctly modifies the verb "goes," indicating the frequency of the action.
• The original phrase "frequent go" is incorrect because "frequent" should be replaced with its adverb form "frequently" to properly modify the verb.
• Let us look at one more example-
• Example- Ramesh frequently goes to the ice cream parlor after having dinner.

Therefore, the correct answer is 'Frequently goes'.

Correct sentence: Mary frequently goes for long drives outside the main city, enjoying the fresh air, the beautiful scenery, and the tranquility that nature provides.

Additional Information

• An adverb is a part of speech that modifies or describes a verb, an adjective, or another adverb.
• Adverbs often provide information about how, when, where, why, or to what extent something happens or is done.
• Example- He ran quickly after he robbed the bank.
• In the above example, The adverb 'quickly' tells us about the verb 'Ran'.

The correct answer is 'Option 3'.

Key Points

• The error lies in the tense inconsistency in the given sentence.
• The verb tense needs to match the past tense of "learned."
• "Is studying" is in the present tense.
• "When" indicates a specific time in the past, so the past continuous tense is needed.
• The correct form of the past continuous tense for "he" is "he was studying."

Therefore, the correct answer is 'He was studying'.

Correct sentence: Murthy learned Classical music from Mr Venkat who is a renowned teacher while he was studying in the fourth grade.

Additional Information

• We have to remember that we have to maintain the tense consistency in any given sentence.
• Example- Rajesh was doing a part-time job while he was in college.
• Option 1 is inappropriate in the given sentence.
• Option 2 is inappropriate in the given sentence.
• Option 4 is inappropriate in the given sentence.

The correct answer is 'Option 2'.

Key Points

• The correct conjunction to use after "No sooner had I finished my final exam" is "than," not "then" or "that."
• In this sentence, "than" is used to contrast the completion of the exam with the invitation to the trip.
• The sentence structure is "No sooner + auxiliary verb + subject + verb + than + subject + verb."
• Example- No sooner had she left the house than it started raining.

Therefore, the correct answer is 'than my friends invited'.

Correct answer: 'No sooner had I finished my office project than my friends invited me to join them on a bike trip to Ladakh'.

Additional Information

• 'When' is used when the sentence starts with 'Hardly', 'Rarely' and 'Scarcely'.
• Example- Hardly had I left the place when she called me back.
• Option 1 is inappropriate in the sentence.
• Option 3 is inappropriate in the sentence.
• Option 4 is inappropriate in the sentence.

The correct answer is 'Option 4'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'often come here' should be used instead of 'often coming here'.
• Often is an adverb meaning ‘many times on different occasions (कई बार अलग-अलग मौकों पर)’.
• The adverb 'often' shows a regular action.
• In this kind of case after the adverb, the base form of the verb is used.

Therefore, the correct answer is 'Often come here'.

Correct sentence: "Suman and his friend often come here after college is over to read books and spend 2 hours.

Additional Information

• Option 1 is inappropriate and grammatically incorrect.
• Option 2 is inappropriate and grammatically incorrect.
• Option 3 is inappropriate and grammatically incorrect.

The correct answer is Option 5.

 

Key Points

• To arrange the jumbled sentences into a meaningful paragraph, we need to identify the introductory sentence, the supporting sentences, and the concluding sentence.
• E: Colossal technology companies, like Google and Amazon, have redefined modern life with their innovative products and services. This sentence acts as a general introduction, presenting the main topic (colossal technology companies) and their overarching impact. It doesn't rely on any prior sentence for context.
• Example: Pioneering scientists, like Marie Curie, redefined our understanding of radioactivity.
• D: These companies often invest heavily in research and development, constantly pushing the boundaries of what's technologically possible. The phrase "These companies" directly refers back to the "Colossal technology companies" introduced in E, explaining their operational approach to innovation.
• A: Their cloud computing infrastructure, for instance, powers countless digital services worldwide. The phrase "for instance" indicates that this sentence provides a specific example of the "innovative products and services" mentioned in E or the "technologically possible" advancements from D.
• B: Moreover, their artificial intelligence and machine learning algorithms underpin everything from search engines to personalized recommendations. "Moreover" signals an addition to the examples given, highlighting another significant technological area.
• C: Consequently, their influence extends far beyond mere consumer electronics, shaping industries and economies globally. "Consequently" indicates a result or conclusion drawn from the pervasive nature of their technology discussed in A and B, summarizing their broad influence.
• Therefore, the logical sequence is E-D-A-B-C.

Therefore, the correct answer is 'Option 5'.

 

Additional Information

• A (Their cloud computing infrastructure, for instance...): Starts with a pronoun ("Their") and a phrase indicating an example ("for instance"), meaning it cannot be the opening sentence.
• B (Moreover, their artificial intelligence...): Starts with a conjunction ("Moreover") which connects it to a previous idea, thus it cannot be the first sentence.
• C (Consequently, their influence...): Starts with a word indicating a consequence ("Consequently"), implying it follows other statements, making it unsuitable as an opener.
• D (These companies often invest...): Starts with a demonstrative pronoun ("These companies") that refers back to a previously mentioned group of companies, so it cannot be the first sentence.

The correct answer is Option 5.

 

Key Points

• To arrange the jumbled sentences into a meaningful paragraph, we need to identify the introductory sentence, the supporting sentences, and the concluding sentence.
• The logical flow is as follows:

1. E: Colossal technology companies, like Google and Amazon, have redefined modern life with their innovative products and services. (This is the best introductory sentence as it introduces the main topic – colossal technology companies – and their overall impact.)
2. D: These companies often invest heavily in research and development, constantly pushing the boundaries of what's technologically possible. (This sentence logically follows E. "These companies" refers back to the "Colossal technology companies" in E, and it explains how they achieve the "innovative products and services" mentioned.)

• Example: Large corporations often invest heavily in R&D to stay competitive.

3. A: Their cloud computing infrastructure, for instance, powers countless digital services worldwide. (This sentence provides the first specific example of their technology, using "for instance" to elaborate on their capabilities.)
4. B: Moreover, their artificial intelligence and machine learning algorithms underpin everything from search engines to personalized recommendations. ("Moreover" signals an additional example of their technological impact, building on the previous one.)
5. C: Consequently, their influence extends far beyond mere consumer electronics, shaping industries and economies globally. ("Consequently" indicates a conclusion or a broader implication derived from the preceding statements about their technology.)

• Based on this logical order (E-D-A-B-C), the second sentence in the paragraph should be D.

Therefore, the correct answer is 'Option 5'.

 

Additional Information

• A (Their cloud computing infrastructure, for instance...): Starts with a pronoun ("Their") and a phrase indicating an example ("for instance"), meaning it cannot be the opening sentence, nor typically the second unless immediately following a general introduction of who "their" refers to, which is not the case here.
• B (Moreover, their artificial intelligence...): Starts with a conjunction ("Moreover") which connects it to a previous idea, thus it cannot be the second sentence.
• C (Consequently, their influence...): Starts with a word indicating a consequence ("Consequently"), implying it follows other statements, making it unsuitable as the second sentence.
• E (Colossal technology companies...): This is the introductory sentence, so it cannot be the second.

The correct answer is Option 1.

 

Key Points

• To arrange the jumbled sentences into a meaningful paragraph, we need to identify the introductory sentence, the supporting sentences, and the concluding sentence.
• The logical flow is as follows:

1. E: Colossal technology companies, like Google and Amazon, have redefined modern life with their innovative products and services. (This is the best introductory sentence as it introduces the main topic – colossal technology companies – and their overall impact.)
2. D: These companies often invest heavily in research and development, constantly pushing the boundaries of what's technologically possible. (This sentence logically follows E. "These companies" refers back to the "Colossal technology companies" in E, and it explains how they achieve the "innovative products and services" mentioned.)
3. A: Their cloud computing infrastructure, for instance, powers countless digital services worldwide. (This sentence provides the first specific example of their technology, using "for instance" to elaborate on their capabilities, directly following the general statement about pushing boundaries.)

• Example: For instance, solar panels convert sunlight into electricity.

4. B: Moreover, their artificial intelligence and machine learning algorithms underpin everything from search engines to personalized recommendations. ("Moreover" signals an additional example of their technological impact, building on the previous one in A.)
5. C: Consequently, their influence extends far beyond mere consumer electronics, shaping industries and economies globally. ("Consequently" indicates a conclusion or a broader implication derived from the preceding statements about their technology.)

• Based on this logical order (E-D-A-B-C), the third sentence in the paragraph should be A.

Therefore, the correct answer is 'Option 1'.

 

Additional Information

• B (Moreover, their artificial intelligence...): Starts with a conjunction ("Moreover"), indicating it is adding to a previous point, so it cannot be the third sentence unless there were two preceding specific examples.
• C (Consequently, their influence...): Starts with a word indicating a consequence ("Consequently"), making it a concluding sentence, not a middle one.
• E (Colossal technology companies...): This is the introductory sentence, so it cannot be the third.
• D (These companies often invest...): This is the second sentence, providing general information after the introduction, but not a specific example, which A provides as the third.

The correct answer is Option 4.

 

Key Points

• To arrange the jumbled sentences into a meaningful paragraph, we need to identify the introductory sentence, the supporting sentences, and the concluding sentence.
• The logical flow is as follows:

1. E: Colossal technology companies, like Google and Amazon, have redefined modern life with their innovative products and services. (This is the best introductory sentence as it introduces the main topic – colossal technology companies – and their overall impact.)
2. D: These companies often invest heavily in research and development, constantly pushing the boundaries of what's technologically possible. (This sentence logically follows E. "These companies" refers back to the "Colossal technology companies" in E, and it explains how they achieve the "innovative products and services" mentioned.)
3. A: Their cloud computing infrastructure, for instance, powers countless digital services worldwide. (This sentence provides the first specific example of their technology, using "for instance" to elaborate on their capabilities, directly following the general statement about pushing boundaries.)
4. B: Moreover, their artificial intelligence and machine learning algorithms underpin everything from search engines to personalized recommendations. ("Moreover" signals an additional example of their technological impact, building on the previous one in A.)

• Example: Moreover, the new policy will improve efficiency.

5. C: Consequently, their influence extends far beyond mere consumer electronics, shaping industries and economies globally. ("Consequently" indicates a conclusion or a broader implication derived from the preceding statements about their technology.)

• Based on this logical order (E-D-A-B-C), the fourth sentence in the paragraph should be B.

Therefore, the correct answer is 'Option 4'.

 

Additional Information

• C (Consequently, their influence...): Starts with a word indicating a consequence ("Consequently"), making it a concluding sentence, generally found at the end of a cohesive paragraph.
• A (Their cloud computing infrastructure, for instance...): This is the third sentence, providing the first specific example.
• D (These companies often invest...): This is the second sentence, providing a general explanation after the introduction.
• E (Colossal technology companies...): This is the introductory sentence, so it cannot be the fourth.

The correct answer is Option 3.

 

Key Points

• To arrange the jumbled sentences into a meaningful paragraph, we need to identify the introductory sentence, the supporting sentences, and the concluding sentence.
• The logical flow is as follows:

1. E: Colossal technology companies, like Google and Amazon, have redefined modern life with their innovative products and services. (This is the best introductory sentence as it introduces the main topic – colossal technology companies – and their overall impact.)
2. D: These companies often invest heavily in research and development, constantly pushing the boundaries of what's technologically possible. (This sentence logically follows E. "These companies" refers back to the "Colossal technology companies" in E, and it explains how they achieve the "innovative products and services" mentioned.)
3. A: Their cloud computing infrastructure, for instance, powers countless digital services worldwide. (This sentence provides the first specific example of their technology, using "for instance" to elaborate on their capabilities, directly following the general statement about pushing boundaries.)
4. B: Moreover, their artificial intelligence and machine learning algorithms underpin everything from search engines to personalized recommendations. ("Moreover" signals an additional example of their technological impact, building on the previous one in A.)
5. C: Consequently, their influence extends far beyond mere consumer electronics, shaping industries and economies globally. ("Consequently" indicates a conclusion or a broader implication derived from the preceding statements about their technology, making it the natural concluding sentence.)

• Example: Consequently, the city implemented new traffic laws.
• Based on this logical order (E-D-A-B-C), the fifth sentence in the paragraph should be C.

Therefore, the correct answer is 'Option 3'.

 

Additional Information

• E (Colossal technology companies...): This is the introductory sentence.
• D (These companies often invest...): This is the second sentence.
• A (Their cloud computing infrastructure, for instance...): This is the third sentence.
• B (Moreover, their artificial intelligence...): This is the fourth sentence.

Common solution:

In P,

Total students = 100%

60% = 180

1% = 3

Total students = 300

Total boys = 40% of 300 = 120

In Q,

Total students = 100%

30% = 120

1% = 4

Total students = 400

Total boys = 70% of 400 = 280

Total students attended the seminar = 40% of 400 = 160

In R,

Total students = 100%

45% = 90

1% = 2

Total students = 200

Total boys = 55% of 200 = 110

In S,

Total students = 100%

40% = 80

1% = 2

Total students = 200

Total boys = 60% of 200 = 120

Total students attended the seminar = 50% of 200 = 100

ATQ**,** Total students not attended the seminar in S = 200 − 100 = 100

 

Calculation:

Required percentage = 100/(180 + 280) x 100 = 21.74% = 22% approx.

Common solution:

In P,

Total students = 100%

60% = 180

1% = 3

Total students = 300

Total boys = 40% of 300 = 120

In Q,

Total students = 100%

30% = 120

1% = 4

Total students = 400

Total boys = 70% of 400 = 280

Total students attended the seminar = 40% of 400 = 160

In R,

Total students = 100%

45% = 90

1% = 2

Total students = 200

Total boys = 55% of 200 = 110

In S,

Total students = 100%

40% = 80

1% = 2

Total students = 200

Total boys = 60% of 200 = 120

Total students attended the seminar = 50% of 200 = 100

ATQ**,** Total students not attended the seminar in S = 200 − 100 = 100

 

Calculation:

ATQ,

In Q, ratio of girls: boys who attended the seminar = 3: 1

Total attended = 160

Boys attended = (1/4) x 160 = 40

In R, ratio of girls: boys who attended the seminar = 3: 2

Total attended = 80

Boys attended = 2/5 x 80 = 32

Required sum = 40 + 32 = 72

Common solution:

In P,

Total students = 100%

60% = 180

1% = 3

Total students = 300

Total boys = 40% of 300 = 120

In Q,

Total students = 100%

30% = 120

1% = 4

Total students = 400

Total boys = 70% of 400 = 280

Total students attended the seminar = 40% of 400 = 160

In R,

Total students = 100%

45% = 90

1% = 2

Total students = 200

Total boys = 55% of 200 = 110

In S,

Total students = 100%

40% = 80

1% = 2

Total students = 200

Total boys = 60% of 200 = 120

Total students attended the seminar = 50% of 200 = 100

ATQ**,** Total students not attended the seminar in S = 200 − 100 = 100

 

Calculation:

ATQ,

Difference between boys and girls in R = 110 – 90 = 20

According to the question,

Girls attended the seminar in Q = 2 × 20 = 40

Total students attended the seminar in Q = 160

Therefore, Boys attended the seminar in Q = 160 – 40 = 120

Total students in R and S together = 200 + 200 = 400

Required ratio = 120:400 = 3:10

Common solution:

In P,

Total students = 100%

60% = 180

1% = 3

Total students = 300

Total boys = 40% of 300 = 120

In Q,

Total students = 100%

30% = 120

1% = 4

Total students = 400

Total boys = 70% of 400 = 280

Total students attended the seminar = 40% of 400 = 160

In R,

Total students = 100%

45% = 90

1% = 2

Total students = 200

Total boys = 55% of 200 = 110

In S,

Total students = 100%

40% = 80

1% = 2

Total students = 200

Total boys = 60% of 200 = 120

Total students attended the seminar = 50% of 200 = 100

ATQ**,** Total students not attended the seminar in S = 200 − 100 = 100

 

Calculation:

ATQ,

Average number of boys in P and S = (120 + 120)/2 = 120

Difference between the students who attended the seminar in P and R = 105 – 80 = 25

Required percentage = (120/25) x 100 = 480%

Common solution:

In P,

Total students = 100%

60% = 180

1% = 3

Total students = 300

Total boys = 40% of 300 = 120

In Q,

Total students = 100%

30% = 120

1% = 4

Total students = 400

Total boys = 70% of 400 = 280

Total students attended the seminar = 40% of 400 = 160

In R,

Total students = 100%

45% = 90

1% = 2

Total students = 200

Total boys = 55% of 200 = 110

In S,

Total students = 100%

40% = 80

1% = 2

Total students = 200

Total boys = 60% of 200 = 120

Total students attended the seminar = 50% of 200 = 100

ATQ**,** Total students not attended the seminar in S = 200 − 100 = 100

 

Calculation:

ATQ,

Ratio of boys: girls in P = 120:180 = 2:3

Boys in E are 20% more than girls in R = 120% of 90 = 108

Thus, boys in E = 108

Since, boys: girls in E = 2: 3

Girls in E = 108 x (3/2) = 162

Shortcut Trick

Effective Compound Interest rate for 2 years (x + y + xy/100).

Scheme X (15%): 15 + 15 + (15 × 15)/100 = 32.25%

Scheme Y (25%): 25 + 25 + (25 × 25)/100 = 56.25%

Difference in interest = 56.25% − 32.25% = 24%

Given 24% of Q = ₹4800 ⇒ Q = 4800 ÷ 0.24 = ₹20000.

∴ The correct answer is ₹20000.

Alternate Method

Given: Principal = ₹Q, Time (n) = 2 years, R_X = 15%, R_Y = 25%

Formula: Amount (A) = P(1 + R/100)ⁿ | Interest (I) = A − P

⇒ Interest from Scheme X = Q[(1 + 15/100)² − 1]

⇒ I_X = Q[(1.15)² − 1] = Q[1.3225 − 1] = 0.3225Q

⇒ Interest from Scheme Y = Q[(1 + 25/100)² − 1]

⇒ I_Y = Q[(1.25)² − 1] = Q[1.5625 − 1] = 0.5625Q

⇒ Difference = 0.5625Q − 0.3225Q = 4800

⇒ 0.24Q = 4800

⇒ Q = 4800 / 0.24 = 20000

∴ The correct answer is ₹20000.

Additional Information

Effective Interest Rate

For 2 years, the total compound interest rate can be calculated as x + y + (xy/100) where x and y are the rates for consecutive years.

Difference between CI and SI

The difference between CI and SI for 2 years on a principal P at R% rate is given by P(R/100)².

Compounding Periods

If interest is compounded half-yearly, the rate becomes R/2 and the time becomes 2n.

Shortcut Trick

Ratio of Profit = Σ(Investment × Time)

A's equivalent capital = (12000 × 3) + (8000 × 9) = 36000 + 72000 = 108000

B's equivalent capital = (18000 × 3) + (24000 × 9) = 54000 + 216000 = 270000

Ratio A : B = 108000 : 270000 = 108 : 270 = 2 : 5

Given A's profit (2 units) = Rs 12000 ⇒ 1 unit = Rs 6000

Total profit (2 + 5 = 7 units) = 7 × 6000 = Rs 42000

∴ The correct answer is Rs 42000.

Alternate Method

Given → A's initial investment = 12000, B's initial investment = 18000. Time = 12 months. Formulas: Profit Share ∝ Investment × Time Period

⇒ A's total investment-month = (12000 × 3) + (8000 × 9) = 1,08,000 ⇒ B's total investment-month = (18000 × 3) + (24000 × 9) = 2,70,000 ⇒ Profit Ratio (A:B) = 108000 : 270000 = 2 : 5 ⇒ Since 2 units = 12000, Total units (2 + 5) = 7 ⇒ Total Profit = (12000 ÷ 2) × 7 = 42000

∴ The correct answer is Rs 42000.

Additional Information

Partnership Basics

In a partnership, profit is distributed based on the product of capital and the time for which it was invested.

Change in Capital

When capital changes during the period, calculate equivalent capital for each duration: (C₁ × T₁) + (C₂ × T₂).

Quantity I

SI for first 2 years = (5000 x 8 x 2)/100 = 800

SI for last 4 years = (5000 x 10 x 4)/100 = 2000

Total SI = 800 + 2000 = 2800

Quantity II = Rs.2400

Hence, Quantity I > Quantity II

Shortcut Trick

Upstream speed (U) = 216 ÷ 6 = 36 kmph.

Stream speed (s) = 25% of Downstream (D) ⇒ s = D/4 ⇒ D = 4s.

As D − U = 2s ⇒ 4s − 36 = 2s ⇒ 2s = 36 ⇒ s = 18 kmph.

D = 4 × 18 = 72 kmph. U = 36 kmph.

Total distance (P + 6) + (P + 72) in 6 hours ⇒ (P + 6)/72 + (P + 72)/36 = 6.

Solving: (P + 6) + 2(P + 72) = 432 ⇒ 3P + 150 = 432 ⇒ 3P = 282 ⇒ P = 94.

∴ The correct answer is 94.

Alternate Method

Given:

Upstream Speed (U) = 216 km ÷ 6 hours = 36 kmph

Stream Speed (s) = 25% of Downstream Speed (D) = D/4

Formula Used:

Downstream Speed (D) = v + s | Upstream Speed (U) = v − s

D − U = 2s | Time = Distance ÷ Speed

Calculations:

⇒ D − 36 = 2 × (D/4)

⇒ D − 36 = D/2

⇒ D/2 = 36 ⇒ D = 72 kmph

⇒ Total Time = (Distance_down/D) + (Distance_up/U)

⇒ 6 = (P + 6)/72 + (P + 72)/36

⇒ 6 × 72 = (P + 6) + 2(P + 72)

⇒ 432 = P + 6 + 2P + 144

⇒ 432 = 3P + 150

⇒ 3P = 282

⇒ P = 94

∴ The correct answer is 94.

Additional Information

Relative Speeds in Water

Speed of boat in still water v = (D + U)/2 and Speed of stream s = (D − U)/2.

Average Speed of Boat

If a boat travels same distance upstream and downstream, Average Speed = (D × U) / v = (v² − s²) / v.

Shortcut Trick

Let the three consecutive multiples of 12 in Set A be x − 12, x, and x + 12.

The largest number in Set A is x + 12, which is also the smallest number in Set B.

The four consecutive odd numbers in Set B are x + 12, x + 14, x + 16, and x + 18.

The average of the smallest numbers in Set A (x − 12) and Set B (x + 12) is [(x − 12) + (x + 12)] ÷ 2 = x = 42.

The 2nd smallest number in Set A is x = 42.

The 2nd largest number in Set B is x + 16 = 42 + 16 = 58.

Required Difference = 58 − 42 = 16.

∴ The correct answer is 16.

Alternate Method

Given:

Set A contains 3 consecutive multiples of 12.

Set B contains 4 consecutive odd numbers.

The largest number of Set A is equal to the smallest number of Set B.

The average of the smallest numbers of Set A and Set B is 42.

Calculations:

⇒ Let the three multiples in Set A be A₁, A₂, and A₃.

⇒ Since they are consecutive multiples of 12: A₁ = A₂ − 12 and A₃ = A₂ + 12.

⇒ Let the four consecutive odd numbers in Set B be B₁, B₂, B₃, and B₄.

⇒ Given that B₁ = A₃ ⇒ B₁ = A₂ + 12.

⇒ The subsequent odd numbers are B₂ = B₁ + 2 = A₂ + 14, B₃ = B₁ + 4 = A₂ + 16, B₄ = B₁ + 6 = A₂ + 18.

⇒ The smallest number in Set A is A₁ = A₂ − 12.

⇒ The smallest number in Set B is B₁ = A₂ + 12.

⇒ Average of smallest numbers = (A₁ + B₁) ÷ 2 = 42

⇒ [(A₂ − 12) + (A₂ + 12)] ÷ 2 = 42

⇒ 2 × A₂ ÷ 2 = 42 ⇒ A₂ = 42

⇒ The 2nd smallest number in Set A is A₂ = 42.

⇒ The 2nd largest number in Set B is B₃ = A₂ + 16 = 42 + 16 = 58.

⇒ Required Difference = B₃ − A₂ = 58 − 42 = 16.

∴ The correct answer is 16.

Additional Information

Consecutive Multiples

Consecutive multiples of a number n have a constant difference of n between any two successive terms.

Consecutive Odd Numbers

Consecutive odd numbers always have a common difference of 2. For example, if the first term is y, the next terms are y + 2, y + 4, and so on.

Averages of Symmetric Sets

The average of two numbers positioned symmetrically around a central value x (like x − d and x + d) is always equal to the central value x.

Common solution:

Total students in A and C = 400 – 160 = 240

Boy/Girls in B = 160/2 = 80

Let boys in A be x.

Or, x + x + 40 + 40 = 240

Or, 2x = 160

So, x = 80

 

In A,

Not appeared boys = 25% of 80 = 20

Appeared boys = 80 – 20 = 60

Not appeared girls = 20 – 5 = 15

Appeared girls = 40 – 15 = 25

In B,

Not appeared boys = 15

Appeared boys = 80 – 15 = 65

Not appeared girls = 81 – (20 + 15 + 15 + 12 + 12) = 7

Appeared girls = 80 – 7 = 73

In C,

Not appeared: Appeared = 1 : 4

Total students = 120

Not appeared students = 120 × (1/5) = 24

Appeared students = 120 – 24 = 96

Not appeared girls = 12

Appeared girls = 80 – 12 = 68

Not appeared boys = 24 – 12 = 12

Appeared boys = 40 – 12 = 28

Calculation:

Students not appeared from C = 12 + 12 = 24

Ratio (D: C not appeared) = 5: 3

Total students in D = 24 x (5/3) = 40

Girls in D = 20% less than boys not appeared from A = 20% less than 20 = 16

Therefore, Boys in D = 40 – 16 = 24

Common solution:

Total students in A and C = 400 – 160 = 240

Boy/Girls in B = 160/2 = 80

Let boys in A be x.

Or, x + x + 40 + 40 = 240

Or, 2x = 160

So, x = 80

 

In A,

Not appeared boys = 25% of 80 = 20

Appeared boys = 80 – 20 = 60

Not appeared girls = 20 – 5 = 15

Appeared girls = 40 – 15 = 25

In B,

Not appeared boys = 15

Appeared boys = 80 – 15 = 65

Not appeared girls = 81 – (20 + 15 + 15 + 12 + 12) = 7

Appeared girls = 80 – 7 = 73

In C,

Not appeared: Appeared = 1 : 4

Total students = 120

Not appeared students = 120 × (1/5) = 24

Appeared students = 120 – 24 = 96

Not appeared girls = 12

Appeared girls = 80 – 12 = 68

Not appeared boys = 24 – 12 = 12

Appeared boys = 40 – 12 = 28

Calculation:

Total boys in A and B together = 80 + 80 = 160

Total girls in C = 80

Required percentage = (160/80) × 100 = 200%

Common solution:

Total students in A and C = 400 – 160 = 240

Boy/Girls in B = 160/2 = 80

Let boys in A be x.

Or, x + x + 40 + 40 = 240

Or, 2x = 160

So, x = 80

 

In A,

Not appeared boys = 25% of 80 = 20

Appeared boys = 80 – 20 = 60

Not appeared girls = 20 – 5 = 15

Appeared girls = 40 – 15 = 25

In B,

Not appeared boys = 15

Appeared boys = 80 – 15 = 65

Not appeared girls = 81 – (20 + 15 + 15 + 12 + 12) = 7

Appeared girls = 80 – 7 = 73

In C,

Not appeared: Appeared = 1 : 4

Total students = 120

Not appeared students = 120 × (1/5) = 24

Appeared students = 120 – 24 = 96

Not appeared girls = 12

Appeared girls = 80 – 12 = 68

Not appeared boys = 24 – 12 = 12

Appeared boys = 40 – 12 = 28

Calculation:

Required difference = (60 + 25) – (15 + 7) = 85 – 22 = 63

Common solution:

Total students in A and C = 400 – 160 = 240

Boy/Girls in B = 160/2 = 80

Let boys in A be x.

Or, x + x + 40 + 40 = 240

Or, 2x = 160

So, x = 80

 

In A,

Not appeared boys = 25% of 80 = 20

Appeared boys = 80 – 20 = 60

Not appeared girls = 20 – 5 = 15

Appeared girls = 40 – 15 = 25

In B,

Not appeared boys = 15

Appeared boys = 80 – 15 = 65

Not appeared girls = 81 – (20 + 15 + 15 + 12 + 12) = 7

Appeared girls = 80 – 7 = 73

In C,

Not appeared: Appeared = 1 : 4

Total students = 120

Not appeared students = 120 × (1/5) = 24

Appeared students = 120 – 24 = 96

Not appeared girls = 12

Appeared girls = 80 – 12 = 68

Not appeared boys = 24 – 12 = 12

Appeared boys = 40 – 12 = 28

Calculation:

Required ratio = (20 + 15): 28 = 35: 28 = 5: 4

Shortcut Trick

Area = 4x × 3x = 12x² = 588 ⇒ x² = 49 ⇒ x = 7 cm.

Perimeter = 2(4x + 3x) = 14x = 14 × 7 = 98 cm.

Circumference = 98 + 34 = 132 cm.

Using 2πr = 132 ⇒ 2 × (22/7) × r = 132 ⇒ r = 21 cm.

Area = (22/7) × 21 × 21 = 1386 cm².

∴ The correct answer is 1386 sq. cm.

Alternate Method

Given: Ratio L:B = 4:3, Area = 588 cm², Circumference (C) = Perimeter (P) + 34 cm.

Formula: Area = L × B; Perimeter = 2(L+B); Circumference = 2πr; Circle Area = πr².

⇒ Let Length = 4x and Breadth = 3x.

⇒ 4x × 3x = 588 ⇒ 12x² = 588 ⇒ x² = 49 ⇒ x = 7.

⇒ Length = 28 cm, Breadth = 21 cm.

⇒ Perimeter = 2(28 + 21) = 2 × 49 = 98 cm.

⇒ Circumference = 98 + 34 = 132 cm.

⇒ 2 × (22/7) × r = 132 ⇒ r = (132 × 7) / 44 = 21 cm.

⇒ Area of Circle = (22/7) × 21 × 21 = 1386 cm².

∴ The correct answer is 1386 sq. cm.

Additional Information

Circle Constants

For a circle with radius 7, the circumference is 44 and area is 154. For radius 21 (3 × 7), the area is 154 × 3² = 1386.

Rectangle Properties

Perimeter is the total length of the boundary: 2(l + b). Area is the product of dimensions: l × b.

Standard π values

Use π ≈ 22/7 for calculations involving multiples of 7 to simplify fractions quickly.

Shortcut Trick

By using the rule of Alligation:

Ratio of Boys to Girls = (66 − 60) : (72 − 66) = 6 : 6 = 1 : 1.

Since the number of boys is 18, the number of girls (X) must also be 18.

∴ The correct answer is 18.

Alternate Method

Given:

Average marks of 18 boys = 72

Average marks of X girls = 60

Combined average marks of all students = 66

Formula Used:

Weighted Average = (N₁ × A₁ + N₂ × A₂) ÷ (N₁ + N₂)

Calculations:

⇒ 66 = (18 × 72 + X × 60) ÷ (18 + X)

⇒ 66 × (18 + X) = 1296 + 60X

⇒ 1188 + 66X = 1296 + 60X

⇒ 66X − 60X = 1296 − 1188

⇒ 6X = 108

⇒ X = 18

∴ The correct answer is 18.

Additional Information

Weighted Average

Used when two or more groups with different averages and quantities are combined into a single group.

Alligation Method

An easier alternative to find the ratio of quantities of ingredients or groups mixed together to produce a desired average mixture value.

Shortcut Trick

Effective Profit% = m − d − (m × d) ÷ 100, where m = Markup% and d = Discount%.

Initial Profit% = 40 − 10 − (40 × 10) ÷ 100 = 30 − 4 = 26%.

Given, 26% of Cost Price (CP) = Rs. 234 ⇒ 1% of CP = 234 ÷ 26 = Rs. 9.

New Profit% (with 25% discount) = 40 − 25 − (40 × 25) ÷ 100 = 15 − 10 = 5%.

New Profit = 5% of CP = 5 × 9 = Rs. 45.

∴ The correct answer is Rs. 45.

Alternate Method

Given: Markup = 40%, Discount₁ = 10%, Profit₁ = Rs. 234, Discount₂ = 25%.

Formulas: MP = CP × (100 + Markup%) ÷ 100 | SP = MP × (100 − Discount%) ÷ 100 | Profit = SP − CP.

⇒ Let Cost Price (CP) = 100 units.

⇒ Marked Price (MP) = 100 + 40% of 100 = 140 units.

⇒ Case 1 Selling Price (SP₁) = 140 − 10% of 140 = 140 − 14 = 126 units.

⇒ Profit₁ = 126 − 100 = 26 units. Given 26 units = Rs. 234 ⇒ 1 unit = Rs. 9.

⇒ Case 2 Selling Price (SP₂) = 140 − 25% of 140 = 140 − 35 = 105 units.

⇒ Profit₂ = 105 − 100 = 5 units.

⇒ Profit in Rupees = 5 × 9 = Rs. 45.

∴ The correct answer is Rs. 45.

Additional Information

Relation between CP and MP

CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%). This ratio is very useful when both discount and profit percentages are known.

Marked Price & Discount

Marked Price is also known as the list price. Discount is always calculated on the MP, while Profit or Loss is always calculated on the CP.

The pattern of the series:

84 – 4² = 68,

68 + 5³ = 193,

193 - 6² = 157,

157 + 7³ = 500,

500 - 8² = 436,

The pattern of the series:

18 + 4³ = 82,

82 + 5³ = 207,

207 + 6³ = 423,

423 + 7³ = 766,

766 + 8³ = 1278

The pattern of the series:

7 + 17² = 296,

296 + 19² = 657,

657 + 21² = 1098,

1098 + 23² = 1627,

1627 + 25² = 2252

Total complaints filed in A = 72

Ratio of complaints filed by Females: Males = 7: 2

Total parts = 7 + 2 = 9

Complaints filed by females = 72 x (7/9) = 56

Given, out of the female complaints, 10 are unaddressed.

Therefore, addressed complaints filed by females = 56 – 10 = 46

Total complaints filed in C = 84

Required difference = 84 – 46 = 38

Total complaints filed in A = 72

Out of these, Robbery complaints = 45

Therefore, Theft complaints = 72 − 45 = 27

Given, 20% of robbery complaints are unaddressed.

Unaddressed robbery complaints = 20% of 45 = 9

Addressed robbery complaints = 45 – 9 = 36

Required difference = 36 – 27 = 9

Total complaints in F = (72 + 48)/2 = 60

Given, Unaddressed in F: Addressed in C = 5: 9

Addressed complaints in C = 54

Unaddressed complaints in F = (5/9) x 54 = 30

Therefore, addressed complaints in F = 60 – 30 = 30

Unaddressed complaints in C and D together = 30 + 18 = 48

Addressed complaints in A and E together = 48 + 36 = 84

Required Ratio = 48:84 = 4:7

Total complaints filed in D and E = 48 + 96 = 144

Total addressed complaints in A and B = 48 + 63 = 111

Required Percentage = (144/111) x 100 = 129.73%

Shortcut Trick

Speed of P = 90 km/hr = 25 m/s. Length of P = (25 × 24) − 300 = 300 m.

Length of Q = 300 ÷ 1.5 = 200 m. Speed of Q = (4/5) × 90 = 72 km/hr = 20 m/s.

Time for Q = (Length of Q + Platform) ÷ Speed of Q = (200 + 520) ÷ 20 = 36 seconds.

∴ The correct answer is 36 seconds.

Alternate Method

Given: Speed of P = 90 km/hr; Bridge = 300 m; Time = 24 s; Ratio Speed P:Q = 5:4; Length P = 1.5 × Length Q.

Formula Used: Distance = Speed × Time; 1 km/hr = 5/18 m/s.

⇒ Speed of Train P in m/s = 90 × (5/18) = 25 m/s

⇒ Total Distance = (Length of P + 300) = 25 × 24 = 600 m

⇒ Length of Train P = 600 − 300 = 300 m

⇒ Length of Train Q = 300 ÷ 1.5 = 200 m

⇒ Speed of Train Q = (4/5) × 90 = 72 km/hr = 72 × (5/18) = 20 m/s

⇒ Time taken by Q = (Length of Q + Platform) ÷ Speed Q = (200 + 520) ÷ 20

⇒ Time = 720 ÷ 20 = 36 seconds

∴ The correct answer is 36 seconds.

Additional Information

Relative Speed

When two trains move in the same direction, relative speed = S₁ − S₂. In the opposite direction, relative speed = S₁ + S₂.

Crossing Objects

When a train crosses a platform, bridge, or another train, total distance covered is the sum of their lengths. If it crosses a pole or person, distance is just the train's length.

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Shortcut Trick

Let Total Work be LCM(18, 9, 6) = 18 units.

Efficiencies: A = 1, B = 2, C = 3.

Work equation: (A + C) × D + B × D = Total Work

(1 + 3) × D + 2 × D = 18 ⇒ 6D = 18 ⇒ D = 3.

Value of 3D = 3 × 3 = 9 days.

∴ The correct answer is 9 days.

Alternate Method

Given: A and C work for D days, and then B works for D days to finish the work.

Calculation:

⇒ Combined efficiency of A and C = 1 + 3 = 4 units/day

⇒ Work done by A and C in D days = 4 × D = 4D units

⇒ Efficiency of B = 2 units/day

⇒ Work done by B in D days = 2 × D = 2D units

⇒ Total work = 4D + 2D = 18 units

⇒ 6D = 18

⇒ D = 3 days

⇒ 3D = 3 × 3 = 9 days

∴ The correct answer is 9 days.

Additional Information

Combined Efficiency

When multiple people work together, their efficiencies (work per day) are added to find the total work done per unit time.

Work-Efficiency Relation

Total Work = Efficiency × Time. Using the LCM method simplifies fractional work into integer units for faster calculation.

Shortcut Trick

Initial ratio of Milk : Water = 7 : 3.

After removing 20 liters and adding 20 liters of Water, new ratio = 7 : 4.

Since only water is added, the Milk units remain constant (7 units).

Increase in water = 4 − 3 = 1 unit → 20 liters.

Total quantity after replacement = (7 + 4) × 20 = 220 liters.

Initial quantity of water = (3/10) × 220 = 66 liters.

∴ The correct answer is 66 liters.

Alternate Method

Given: Initial Ratio = 7 : 3, Replaced Quantity = 20 liters, Final Ratio = 7 : 4.

Formula: Quantity of Milk = Initial Total × (7/10). Replacement keeps total volume constant.

⇒ Let initial total quantity be Q liters. Initial Milk = 0.7Q, Initial Water = 0.3Q.⇒ Milk removed = 20 × (7/10) = 14 liters. Water removed = 20 × (3/10) = 6 liters.⇒ New Milk = 0.7Q − 14. New Water = 0.3Q − 6 + 20 = 0.3Q + 14.⇒ (0.7Q − 14) / (0.3Q + 14) = 7 / 4⇒ 4 × (0.7Q − 14) = 7 × (0.3Q + 14)⇒ 2.8Q − 56 = 2.1Q + 98⇒ 0.7Q = 154⇒ Q = 154 / 0.7 = 220 liters.⇒ Initial Water = 0.3 × 220 = 66 liters.

∴ The correct answer is 66 liters.

Additional Information

Mixture Replacement Rule

When a portion of mixture is replaced by one of its components, the component not added remains constant in the ratio comparison.

Initial Quantity Formula

Final Quantity = Initial Quantity × (1 − replaced volume / total volume)ⁿ for repeated replacements of a single component.

Alligation in Replacement

Replacement problems can also be solved by treating the added pure component as a 100% concentration mixture.

Shortcut Trick

The age difference between two people remains constant at any point in time.

Difference after 6 years = 6 years ⇒ Difference 3 years ago = 6 years.

Ratio 3 years ago (P : Q) = 7 : 9 ⇒ Ratio difference = 2 units.

2 units = 6 years ⇒ 1 unit = 3 years.

Q age 3 years ago = 9 × 3 = 27 years → Present age = 27 + 3 = 30 years.

∴ The correct answer is 30 years.

Alternate Method

Given: Ratio of P : Q (3 years ago) = 7 : 9. Condition after 6 years: Q = P + 6.

Method Used: Linear equations and age difference property.

⇒ Let ages 3 years ago be P = 7x and Q = 9x.

⇒ Present ages: P = 7x + 3, Q = 9x + 3.

⇒ Ages after 6 years: P = 7x + 3 + 6 = 7x + 9, Q = 9x + 3 + 6 = 9x + 9.

⇒ According to question: (9x + 9) − (7x + 9) = 6.

⇒ 2x = 6 ⇒ x = 3.

⇒ Present age of Q = 9x + 3 = 9(3) + 3 = 27 + 3 = 30.

∴ The correct answer is 30 years.

Additional Information

Constant Age Difference

The difference between the ages of two persons remains the same throughout their lives. If Q is 6 years older than P today, Q will always be 6 years older.

Ratio Balancing Method

When the age difference is known, the difference between the ratio parts can be directly equated to the real-time difference (e.g., Difference in ratio units = Real age difference).

Shortcut Trick

Let Total Income be 100 units.

Household = 30 units; Remaining = 70 units.

Shopping = 20% of 70 = 14 units; Remaining after shopping = 56 units.

Fixed Deposit (FD) = 3/5 × 56 = 33.6 units.

Difference (FD − Shopping) = 33.6 − 14 = 19.6 units → ₹1960. ∴ 1 unit = ₹100.

∴ The correct answer is ₹10000.

Alternate Method

Given: Household expenses = 30%, Shopping = 20% of remaining, MF : FD = 2 : 3.

⇒ Let Income = I

⇒ Remaining income after household = I − 0.30I = 0.70I

⇒ Amount spent on shopping = 20% of 0.70I = 0.14I

⇒ Remaining income after shopping = 0.70I − 0.14I = 0.56I

⇒ Amount in Fixed Deposits (FD) = 3 / (2 + 3) × 0.56I = 0.6 × 0.56I = 0.336I

⇒ Difference (FD − Shopping) = 0.336I − 0.14I = 0.196I

⇒ 0.196I = 1960

⇒ I = 1960 ÷ 0.196 = 10000

∴ The correct answer is ₹10000.

Additional Information

Percentage of Remaining

When spending from the remaining balance, multiply the current balance by (100 − x) / 100 to find the new balance.

Ratio Distribution

To divide a quantity Q in ratio a : b, the parts are [a / (a + b)] × Q and [b / (a + b)] × Q.

Base Change Rule

Always identify the base of the percentage. If it says 'of the remaining', the base is the balance after previous subtractions.

Given: Seven persons- L, M, N, O, P, Q and R are standing in a linear row such that all are facing the north. Each person uses mobile of different mobiles - Oppo, Vivo, Samsung, Apple, Xiaomi, Realme and Oneplus. All the information is not necessarily in the same order.

1. M uses Realme and stands second from the end. 
2. Only two persons stand between M and L. 
3. The one who uses Oppo stands immediate right of L. 

Here, we have 2 Cases, i.e., Case 1 and Case 2.

4. The number of persons standing towards the left of the one who uses Oppo is one more than the number of persons standing towards the right of N. 

5. Only three persons stand between N and the one who uses Xiaomi. 

6. P is an immediate neighbor of the one who uses Xiaomi. 

7. More than two persons stand between P and the one who uses Vivo. R uses Apple. 

8. The one who uses Oneplus stands second to the right of O. 

Case 1 is eliminated because R uses Apple and there is no space for R. So, Case 2 is the final arrangement.

The one who stands second to the left of Q uses Samsung.

Hence, the correct answer is 'The one who stands second to the left of Q'.