SBI PO Prelims Memory Based Paper (Held On: 4 November 2023 Shift 4) (Previous Year Paper)

The correct answer is option 5.

Key Points

• The given sentence talks about attackers using technology to engage in various activities such as phone scams and posting fake videos on social media platforms that are against the law.
• Therefore, the most appropriate word for the given blank would be 'illegal'.
• Also, the word 'defraud' indicates the use of the word 'illegal' in the given blank.
• 'illegal' means contrary to or forbidden by law, especially criminal law. (गैरकानूनी)
• For Example -
• It is illegal to intercept radio messages.
• Hence, the correct answer is 'illegal'.

​

The complete sentence would be - Attackers are using technology to defraud users, steal their identity, and to engage in various other illegal activities like phone scams and posting fake videos on social media platforms.

 Additional Information

Let's understand the meanings of the other given options -

• Encouraging means giving someone support or confidence; supportive. (उत्साहजनक)
• Ethical means to be morally good or correct. (नैतिक)
• Scrambled means to struggle or compete with others for something in an eager or uncontrolled and undignified way. (संघर्ष)
• Regressive means returning to a former or less developed state; characterized by regression. (प्रतिगामी)

The correct answer is option 3.

Key Points

• The given sentence talks about PM Modi urging global investors to explore investment opportunities in India.
• Therefore, the most appropriate word for the given blank would be 'opportune'.
• Also, the word 'opportunities' indicates the use of the word 'opportune' in the given blank.
• 'Opportune' means to be especially convenient or appropriate for a particular action or event. (समयानुकूल)
• For Example -
• She was waiting for an opportune moment to ask for help.
• Hence, the correct answer is 'opportune'.

 

The complete sentence would be - Prime Minister Narendra Modi urged global investors to explore investment opportunities in the country’s energy sector, saying India is the most opportune place at present.

 

Additional Information

Let's understand the meanings of the other given options -

• Exquisite means to be extremely beautiful and delicate. (उत्कृष्ट)
• Forbidden means to be not allowed; banned. (निषिद्ध)
• Permitted means to officially allow (someone) to do something. (अनुमति है)
• Ambiguous means to be open to more than one interpretation; not having one obvious meaning. (अस्पष्ट)

The correct answer is option 4.

Key Points

• The given sentence talks about the budget aiming to fulfil the long-term goals of India and being the world’s fastest-growing large economy.
• Therefore, the most appropriate word for the given blank would be 'sustainable'.
• 'Sustainable' means able to be maintained at a certain rate or level. (दीर्घकालिक)
• For Example -
• The government is working on making the energy sector sustainable.
• Hence, the correct answer is 'sustainable'.

 

The complete sentence would be - The Budget aims to fulfil the long-term sustainable goals of the country along with being the world’s fastest-growing large economy. 

Additional Information

Let's understand the meanings of the other given options -

• Implausible means not seeming reasonable or probable; failing to convince. (अकल्पनीय)
• Challenging means testing one's abilities; demanding. (चुनौतीपूर्ण)
• Obnoxious means to be extremely unpleasant. (घृणित)
• Untenable means not able to be maintained or defended against attack or objection. (अस्थिर, असमर्थनीय)

The correct answer is option 1.

Key Points

• The given sentence talks about the subject (He) being arrogant and making people feel like he has a lot of money in his bank account.
• Therefore, the most appropriate word for the given blank would be 'exaggerate'.
• 'Exaggerate' means to represent (something) as being larger, better, or worse than it really is. (अतिशयोक्ति)
• For Example -
• He always exaggerates his accomplishments.
• Hence, the correct answer is 'exaggerate'.

The complete sentence would be - He is an arrogant businessman and he likes to exaggerate his net worth, it makes him seem like he has a lot of money in his bank account.

Additional Information

Let's understand the meanings of the other given options -

• Propel means to drive or push something forwards. (प्रेरित करना)
• Compensate means to give (someone) something, typically money, in recognition of loss, suffering, or injury incurred; recompense. (मुआवजा देना)
• Understate means to describe or represent (something) as being smaller or less good or important than it really is. (कम बतलाना)
• Trivialize means to make (something) seem less important, significant, or complex than it really is. (महत्वहीन)

The correct answer is B-D.

Key Points

• The sentence talks about how the world-famous heritage sites of Ajanta and Ellora, and other tourist spots in the district will remain shut on Saturdays and Sundays, while marriages will not be allowed to be held in function halls during the lockdown period.
• Looking at the sentence, we can find that:
• In part B, 'officials' spot is inappropriate. Instead, 'tourist' from part D seems more inappropriate in this part of the sentence.
• In part D, we can assume that only officials are in a place to issue statements and not tourists. Therefore, 'officials' will replace 'tourists' in part D.
• 'and other tourists' and 'officials said' are both grammatically and contextually correct.
• Therefore B replaces D and vice-versa.
• Thus, the correct answer is option 1.

The correct answer is: The world-famous heritage sites of Ajanta and Ellora, and other tourist spots in the district will also remain shut on Saturdays and Sundays, while marriages will not be allowed to be held in function halls during the lockdown period, officials said.

The correct answer is A-D.

Key Points

• Looking at the sentence, we can see that
• If A were correct, it should have been 'students''- the possessive form in place of 'students'. Therefore, 'students' is incorrect in part A.
• 'Continuing' is a verb. So, 'continuing' will not fit in part D. Instead, it has to be replaced with a noun i.e 'student
• 'Continuing professional development' and 'creatively with their students' are both grammatically and contextually correct.
• Therefore, A will replace D and vice-versa.
• Thus, the correct answer is option 2.

 The correct sentence is: Continuing professional development is necessary to innovate and engage creatively with their students.

The correct answer is A-C

Key Points

• The sentence talks about how a well-known adage in the education world is that technology cannot replace a teacher but a teacher who uses technology will replace one who does not*.*
• Looking at the sentence, we can find that:
• In part A, 'teacher world' doesn't sound correct. Therefore, we can see in part C, that the word 'education' can replace 'teacher' perfectly.
• In part C, we can see that the article 'a' doesn't go with 'education'. Therefore, we can replace 'education' with 'teacher' and it will make sense
• Therefore, 'adage in the education world' and 'but a teacher who uses' are both grammatically and contextually correct.
• Therefore, A replaces C and vice-versa.
• Thus the correct answer is option 4.

                                                

The correct sentence is: A well-known adage in the education world is that technology cannot replace a teacher but a teacher who uses technology will replace one who does not.

The correct answer is A- C.

Key Points

• Let us look at the given sentence in the following manner - 
• The study also ____ (A) the ____ (B) of Head Start programs that use a ____ (C) educational ____ (D).
• To understand which word belongs in which blank we need to know its meaning as enlisted below -

• From the above meanings it is clear that
• the study also different is an incorrect phrase.
• As 'examined' starts with a vowel, it cannot come after the article 'a'.
• So, A and C should be interchanged to make the sentence correct.

Therefore the correct sentence is - The study also examined the effect of Head Start programs that use a different educational approach.

The correct answer is A-B.

Key Points

• Let us look at the given sentence in the following manner -

In the rural ____ (A), there was less ____ (B) with traffic, although an ____ (C) farm dog forced him to ____ (D) his sprints.

• To understand which word belongs in which blank we need to know its meaning as enlisted below -

 

• From the above meanings it is clear that
• the rural concern is an incorrect phrase.
• Individually the phrase 'was less areas' might sound correct. But in context of the given sentence it does not fit.
• So, A and B should be interchanged to make the sentence correct.

Therefore the correct sentence is - In the rural areas, there was less concern with traffic, although an occasional farm dog forced him to practice his sprints.

Confusion Points

• The phrase 'there was less areas with traffic' might sound conceptually correct.
• But grammatically it is wrong.
• It voids subject-verb agreement. Was is singular while areas is plural.

The correct answer is option 3.

Key Points

Part C of the sentence i.e. 'day I had the most tastiest' is erroneous.

• In part C of the sentence, the use of the adverb 'most' before the adjective 'tastiest' is superfluous.
• The adjective 'taste' is already given in its superlative form i.e. tastiest and does not need to be preceded by 'most'.
• Hence, the correct answer is C.
• The correct sentence would be - When I went wine tasting with my friends the other day I had the tastiest wine that I have ever had.

​

Additional Information

Difference between adjectives and adverbs - 

• Adjective - An adjective is a word that modifies or describes a noun or pronoun. Adjectives can be used to describe the qualities of someone or something independently or in comparison to something else.
• For Example -
• She wore a beautiful dress at her birthday party.
• Adverb - An adverb is a word that modifies (describes) a verb (he sings loudly), an adjective (very tall), another adverb (ended too quickly), or even a whole sentence (Fortunately, I had brought an umbrella). Adverbs often end in –ly, but some (such as fast) look exactly the same as their adjective counterparts.
• For Example -
• She was beautifully dressed at her birthday party.

The correct answer is option 1.

Key Points

Part A of the sentence i.e. 'As it is to be superior than' is erroneous.

• Here, the preposition 'than' used after the adjective 'superior' is incorrect and it should be replaced with the preposition 'to'.
• As per English Grammar rules, the adjectives inferior, superior, senior, junior, prior etc. take the preposition 'to' not 'than'.
• For Example -
• The air hostess asked all the passengers to fasten their seat belts prior to descent.
• You can give this task to someone junior to you.
• Hence, the correct answer is A.
• The correct sentence would be - As it is to be superior to static graphics, animation is being increasingly employed in technology-based learning resources.

​

Additional Information

Let's understand the use of the prepositions 'to' and 'than' - 

To - 

• It is used to indicate the place, person, or thing that someone or something moves toward, or the direction of something.
• For Example -
• We went to the shopping mall.
• It is used to indicate a limit or an ending point.
• For Example -
• The clothes were piled up to the roof in the cupboard.
• It is used to indicate the relationship between two things.
• For Example -
• Your time is very important to us.
• It is also used to indicate a time or a period.
• For Example -
• I work from nine to five on weekdays.

 

Than - 

• It is used used for comparing and to introduce the second part of a comparison.
• For Example -
• I like cake more than pie.

The correct answer is option 2.

Key Points

Part B of the sentence i.e. 'depend on how individuals and' is erroneous.

• Here, the verb 'depend' is given in its base form while it should be used with an 's' at the end of it.
• As per English Grammar rules, In the simple present tense, the verb with the third-person singular subject is used with s/es at the end of it.
• For Example -
• He cooks his breakfast every morning.
• Hence, the correct answer is B.
• The correct sentence would be - The transition to a circular economy depends on how individuals and organisations learn to innovate and apply what they have learned in the real world.

​

Additional Information

Sentence structure of the present simple tense - 

Singular subject -

• Subject + Verb in its base form + s/es + Object 
• For Example -
• He cooks dinner every day.

Plural subject - 

• Subject + Verb in its base form + Object 
• For Example -
• They usually wake up early in the morning

The correct answer is option 4.

Key Points

Part D of the sentence i.e. 'and creating innovation platforms for digital banking' is erroneous.

• The noun 'innovation' given before the noun 'platforms' is incorrect and it should be replaced with the adjective 'innovative'.
• Adjective - Adjectives are words that come before nouns to describe the the qualities or states of being of nouns. 
• For Example -
• Your have a very beautiful collection of clothes.
• Hence, the correct answer is D.
• The correct sentence would be - This was only possible because India has made financial inclusion a priority, investing in a digital ID system called Aadhaar and creating innovative platforms for digital banking.

​

Additional Information

Difference between noun and adjective - 

• Noun - A noun is a word that represents a person, place, thing, or idea. It can function as a subject, object, or complement in a sentence. Examples of nouns include - dog, house, book, etc.
• Adjective - An adjective, on the other hand, is a word that describes or modifies a noun or pronoun. It provides additional information about the noun by indicating its quality, size, colour, or other characteristics. Examples of adjectives include - red, beautiful, happy, etc.

 

To see the difference between a noun and an adjective in action, consider the following sentences -

• The dog barked at the mailman. (dog is a noun)
• The brown dog barked at the mailman. (brown is an adjective that modifies the noun dog)

In the first sentence, the noun dog is the subject of the sentence, while in the second sentence, the adjective brown provides additional information about the dog's color.

The correct answer is 'No error'.

Key Points 

• There is no error in the given sentence.
• The verb "was" in segment (C) is correct, as it refers back to the singular "the solar cooker".
• If it were referring to multiple cookers, we would use "were".
• 'to transform household energy consumption' is additional information.
• 'fabricated' is a verb which means construct or manufacture (an industrial product), especially from prepared components. 
• ​Example:- "you will have to fabricate an exhaust system"
• The use of subject-verb agreement is absolutely correct.
• Hence, the given sentence is correct.

Hence, option 5 is the correct answer.

Confusion Points

• Amid and Amidst are two words that look very similar. Believe it or not, these words mean the same thing.
• Both mean to be in the middle of something or surrounded by something.
• Although these two words are interchangeable, the word amid is more commonly used.

The correct answer is E.

Key Points

• The first sentence is E as it is introducing the topic by mentioning about a meeting.
• The second sentence is D as it mentions that the deputy government also attended the meeting.
• The third sentence is B as it mentions what was said at the meeting.
• The fourth sentence is C. It informs that some other issues were also discussed at the meeting.
• The last sentence is A as it is concluding the passage by mentioning the purpose behind the discussion of these issues.
• Thus the correct sequence is EDBCA.
• The first sentence is E.

Additional Information

Concern: to relate to or to worry

Regulator: a person or body that supervises a certain industry

Assessment: evaluation or judgement

The correct answer is B.

• The first sentence is E as it is introducing the topic by mentioning about a meeting.
• The second sentence is D as it mentions that the deputy government also attended the meeting.
• The third sentence is B as it mentions what was said at the meeting.
• The fourth sentence is C. It informs that some other issues were also discussed at the meeting.
• The last sentence is A as it is concluding the passage by mentioning the purpose behind the discussion of these issues.
• Thus the correct sequence is EDBCA.
• The third sentence is B.

Concern: to relate to or to worry

Regulator: a person or body that supervises a certain industry

Assessment: evaluation or judgement

The correct answer is C.

• The first sentence is E as it is introducing the topic by mentioning about a meeting.
• The second sentence is D as it mentions that the deputy government also attended the meeting.
• The third sentence is B as it mentions what was said at the meeting.
• The fourth sentence is C. It informs that some other issues were also discussed at the meeting.
• The last sentence is A as it is concluding the passage by mentioning the purpose behind the discussion of these issues.
• Thus the correct sequence is EDBCA.
• The fourth sentence is C.

Concern: to relate to or to worry

Regulator: a person or body that supervises a certain industry

Assessment: evaluation or judgement

The correct answer is A.

• The first sentence is E as it is introducing the topic by mentioning about a meeting.
• The second sentence is D as it mentions that the deputy government also attended the meeting.
• The third sentence is B as it mentions what was said at the meeting.
• The fourth sentence is C. It informs that some other issues were also discussed at the meeting.
• The last sentence is A as it is concluding the passage by mentioning the purpose behind the discussion of these issues.
• Thus the correct sequence is EDBCA.
• The fifth sentence is A.

Concern: to relate to or to worry

Regulator: a person or body that supervises a certain industry

Assessment: evaluation or judgement

The correct answer is D.

• The first sentence is E as it is introducing the topic by mentioning about a meeting.
• The second sentence is D as it mentions that the deputy government also attended the meeting.
• The third sentence is B as it mentions what was said at the meeting.
• The fourth sentence is C. It informs that some other issues were also discussed at the meeting.
• The last sentence is A as it is concluding the passage by mentioning the purpose behind the discussion of these issues.
• Thus the correct sequence is EDBCA.
• The second sentence is D.

Concern: to relate to or to worry

Regulator: a person or body that supervises a certain industry

Assessment: evaluation or judgement

The correct answer is 'Only B.'

Key Points

• The given word 'Intimidating' means to frighten or threaten somebody, often in order to make him or her do something. (डराने वाला, धमकी भरा, अभित्रासकीय)
• Let us explore the given sentences:
• The word 'revert' should be used in the first sentence as it talks about the state court's refusal to change back the local court’s decision.
• The word 'revert' means to return to a previous state, practice, topic, etc. (पूर्व दशा या क्रिया में लौट जाना)
• The word 'intimidating' is used correctly in the second sentence as it talks about how learning to use a computer was frightening for the retiree.
• Example: Government officials accused the rebels of intimidating voters.
• The word 'jerk' should be used in the third sentence as it talks about the sudden movement of the airplane due to stormy weather.
• The word 'jerk' means a sharp, sudden movement. (झटका)
• Therefore, only sentence B best expresses the meaning of the given word.

Hence, the correct answer is option 4.

Sentence A: The state court refused to revert the local court’s decision.

Sentence B: Learning to use a computer was intimidating for the retiree as she was afraid she wouldn't be able to understand the new technology.

Sentence C: As the stormy weather began to worsen, the airplane began to jerk back and forth.

The correct answer is 'Both A and C.'

Key Points

• The given word 'Optimistic' means hopeful and confident about the future. (स्थितियों की अनुकूलता या प्रयत्‍नों में सफलता की आशा करने वाला; आशापूर्ण, आशान्वित)
• Let us explore the given sentences:
• The word 'optimistic' is used correctly in the first sentence as it talks about a graduate who is hopeful that he will find a job soon.
• Example: I am very optimistic about our chances of success.
• The word 'drastic' should be used in the second sentence as it talks about the extreme or very strong effects of the drought.
• The word 'drastic' means extreme, and having a sudden very strong effect. (अत्‍यधिक और भरपूर असरदार, उग्र, प्रचंड)
• The word 'optimistic' is used correctly in the third sentence as it talks about a team that is confident about winning the game.
• Example: Despite all the difficulties, he still remains optimistic.
• Therefore, both A and C best express the meaning of the given word.

Hence, the correct answer is option 2.

Sentence A: Optimistic about the future, the recent graduate just knew that he would find a job soon.

Sentence B: The effects of the drought were so drastic that everyone was without clean water.

Sentence C: Though we haven’t won a game all year, our team is still optimistic that today we will win.

The correct answer is option 3.

Key Points

• To answer this question, let's first understand the meaning of the given word -
• Incentive - (Noun) - a thing that motivates or encourages someone to do something, a payment or concession to stimulate greater output or investment (प्रोत्साहन)
• For Example -
• Students receive a certificate as an incentive for their outstanding academic performance.
• After understanding the meaning of the given word, we can conclude that "incentive" is used correctly in only sentence B (as a noun), while both sentences A and C are incorrect.
• Sentence A - Consider taking a break to gain a fresh incentive on the problem.
• This sentence is incorrect because "incentive" is not the right word here. "Incentive" means motivation, whereas the context requires "perspective," which means a fresh way of looking at something.
• Sentence C - The company conducted incentive market research to understand customer preferences.
• This sentence is incorrect because "incentive" implies motivation or rewards, which doesn't fit the context. We should replace it with "extensive" to convey the intended meaning of comprehensive market research.
• Therefore, the correct answer is "Only B."

The correct answer is option 5.

Key Points

• To answer this question, let's first understand the meaning of the given word -
• Dispatch - (Noun) - the sending of someone or something to a destination or for a purpose, promptness and efficiency, an official report on state or military affairs (भेजना)
• For Example -
• The dispatch of the urgent message reached the recipient within minutes.
• Dispatch - (Verb) - send off to a destination or for a purpose
• For Example -
• It's essential to dispatch these tasks efficiently to meet our deadlines.
• After understanding the meaning of the given word, we can conclude that "dispatch" is used correctly in all three sentences.
• Therefore, the correct answer is "All A, B & C."

The correct answer is option C.

Key Points

• The word profound is used in the passage to describe the effects that dietary habits have on health.
• In English, "profound" typically means very great or intense. In the context of the passage, it refers to deep and significant effects.
• Profound in Hindi: गहरा (Gahra)
• The provided options were:
• A. Insignificant - नगण्य (Naganya)
• B. Superficial - सतही (Satahi)
• C. Deep - गहरा (Gahra)
• D. Unnoticeable - अदृश्य (Adrishya)
• E. Sudden - अचानक (Achanak)
• Given the context, option C (Deep - गहरा) is the correct translation and meaning of "profound."

The correct answer is option A.

Key Points

• The term holistic in the passage is used to describe an approach to health that considers all aspects of a person's life.
• होलिस्टिक (Holistic) means encompassing the whole of something, or the complete systems rather than with their parts.
• Holistic in Hindi: समग्र (Samagra)
• The provided options were:
• A. Focused on a single aspect - एकल पहलू पर केंद्रित (Ekal Pehlu Par Kendrit)
• B. Fragmented - खंडित (Khandit)
• C. Comprehensive - समग्र (Samagra)
• D. Traditional - पारंपरिक (Paramparik)
• E. Quick-fix - त्वरित समाधान (Twarit Samadhan)
• Option A (Comprehensive - समग्र) correctly reflects the meaning of holistic in the context used within the passage.

The correct answer is option B.

Key Points

• The passage extensively discusses the profound effects that dietary habits have on individual health, indicating that the focus is on understanding the broader impacts of diet.
• Options A, C, D, and E mention specific aspects or types of diets, which the passage does not focus on in detail.
• Therefore, the most comprehensive and fitting answer is B, highlighting the general impact of diet on health.

The correct answer is option B.

Key Points

• The passage mentions a holistic approach to health, suggesting that all factors, including physical, mental, and emotional, should be considered in dietary choices.
• This comprehensive approach aligns directly with option B.
• Other options are either too specific or unrelated to the holistic theme discussed in the passage.

The correct answer is option C.

Key Points

• The passage highlights the importance of a balanced diet that includes necessary nutrients like dietary fibers.
• While specific roles of fibers are not detailed in the provided text, generally, dietary fibers are known to support digestion and cardiovascular health, aligning with a statement about contributing to various health aspects.
• Options A, D, and E are incorrect based on general nutritional knowledge, and B is too narrow in scope compared to what is implied in the passage.

The correct answer is option C.

Key Points

• Statement A: "A high-carb diet is ideal for all." This statement is false as the passage emphasizes the need for a balanced diet that includes not just carbohydrates but also proteins, fats, and other nutrients, highlighting that diet needs are individual and should be tailored.
• Statement B: "Nutritional science supports a one-size-fits-all diet approach." This statement is false; the passage clearly supports the idea that dietary needs vary among individuals, and nutritional science favors personalized diet plans based on individual health needs and lifestyle factors.
• Statement C: "Diets should balance carbohydrates, proteins, and fats." This is true and directly supported by the passage, which advocates for a balanced diet that includes a variety of nutrients to maintain overall health and support different body functions.
• Statement D: "Nutrients have no impact on mental health." This statement is false according to the passage, which links diet not only to physical health but also to mental and emotional well-being, underscoring the impact of nutrients like omega-3 fatty acids on brain health.
• Statement E: "Diet plans should exclude all fats." This statement is false; the passage indicates the importance of including healthy fats in the diet, which are vital for various bodily functions and maintaining overall health.

The correct answer is option C.

Key Points

• Statement A: "Dietary habits significantly influence individual health." This statement is true as the passage discusses the various impacts of diet on different aspects of health, emphasizing that diet is a key component of maintaining good health.
• Statement B: "A balanced diet should include a variety of nutrients." This is true according to the passage, which notes the importance of a well-rounded diet incorporating different nutrients to support overall health.
• Statement C: "All diets should primarily focus on weight loss." This statement is false in the context of the passage. The passage promotes a holistic approach to dieting that considers physical, mental, and emotional health, not solely weight loss.
• Statement D: "Dietary fibers contribute to health." True, as indicated in the passage, dietary fibers play a significant role in maintaining health, supporting digestion, and other functions.
• Statement E: "A holistic diet approach is beneficial for overall well-being." This statement is true and mirrors the passage's central theme that a diet should be comprehensive and consider various health dimensions.

By analyzing the given statements with reference to the passage, it becomes clear that the only statement not aligned with the passage's emphasis on a comprehensive dietary approach is option C. It incorrectly focuses solely on weight loss, whereas the passage advocates for a broader perspective on health.

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

Number of males studying in college A from city P = 360 ×  (60/100) = 216

Number of males studying in college A from city Q = (360 - 216) = 144

Number of males studying in college C from city P =250 ×  (80/100) = 200

Number of males studying in college C from city Q = (250 - 200) = 50

Number of females studying in college A from city P = 180 ×  (25/100) = 45

Number of females studying in college A from city Q = (180 - 45) = 135

Number of females studying in college C from city P = 200 ×  (30/100) = 60

Number of females studying in college C from city Q = 200 - 60 = 140

Required total = (144 + 50 + 135 + 140) = 469

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

Number of males studying in college B = 390

Number of males studying in college B secured distinction = 390 ×  1/3 = 130

Number of males secured first class and second class in college B  = (390 - 130) = 260

Number of females studying in college B = 300

Number of females studying in college B secured distinction = 300 ×  1/6 = 50

Number of females secured first class and second class in college B = (300 - 50) = 250

Total secured first class and second class = 260 + 250 = 510

Number of students secured first class = 510/3 ×  2 = 340

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

Number of males studying in college D = 360

Number of females studying in college D = 240

Exam fees for males  semester exam = Rs. 350

Exam fees for females in semester exam = Rs. 250

Total fees collected = (360 ×  350 + 240 ×  250) = (126000 + 60000)

Total collected = Rs. 186000

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

1/3^rd of number of males studying in college D = 360 ×  1/3 = 120

1/4 th of the number of males studying in college E = 576 × 1/6 = 96

1/6 th of the number of females studying in college D = 240 ×  1/6 = 40

1/8 th of the number of females studying in college E = 144 × 1/8 =  18

Required difference = (120 + 96) - (40 + 18) = (216 - 58) = 158

General solution:

Number of students studying in college E = 720

Value of Y = 720/3000 ×  100 = 24%

To find the value of Y

(24% + (24 - 4)% + (X - 3)% + 23% +X%) = 100%

(64% + 2X%) = 100%

2X% = 36%

X = 18%

College A:

Number of students studying in college A = 3000 × (18/100) = 540

Number of males studying in college A = 540/3 ×  2 = 360

Number of females studying in college A = (540 - 360) = 180

 

College B:

Number of students studying in college B = 3000 × (23/100) = 690

Number of males studying in college B = 690/23 ×  13 = 390

Number of females studying in college B = (690 - 390) = 300

 

College C:

Number of students studying in college C = 3000 × (15/100) = 450

Number of males studying in college C = 450/9 ×  5 = 250

Number of females studying in college C = (450 - 250) = 200

 

College D:

Number of students studying in college D = 3000 × (20/100) = 600

Number of males studying in college D = 600/5 ×  3 = 360

Number of females studying in college D = (600 - 360) = 240

 

College E:

Number of students studying in college E = 3000 × (24/100) = 720

Number of males studying in college E = 720/5 ×  4 = 576

Number of females studying in college E = (720 - 576) = 144

 

Solution:

Number of males studying in college C = 250

Number of males studying in college D = 360

Number of females studying in college A = 180

Number of females studying in college B = 300

Required ratio = (250 + 360): (180 + 300) = (610: 480) = 61 : 48

Shortcut Trick

Let total members be 100%.

Remaining after Amazon Prime (20%) = 80%.

Remaining after Netflix (50% of 80%) = 40%.

Remaining after Hotstar (30% of 40%) = 40% − 12% = 28%.

28% = 6300 ⇒ 1% = 225 ⇒ 100% = 22500.

∴ The correct answer is 22500 members.

Alternate Method

Let total members be x.

⇒ Amazon Prime users = 20% of x = 0.20x

⇒ Remaining after Amazon = x − 0.20x = 0.80x

⇒ Netflix users = 50% of 0.80x = 0.40x

⇒ Remaining after Netflix = 0.80x − 0.40x = 0.40x

⇒ Hotstar users = 30% of 0.40x = 0.12x

⇒ Remaining (Youtube) = 0.40x − 0.12x = 0.28x

⇒ 0.28x = 6300

⇒ x = 6300 ÷ 0.28 = 22500

∴ The correct answer is 22500 members.

Additional Information

Successive Percentage Decrease

When values are deducted from the 'remaining' part, it follows a successive pattern: Final Value = Initial Value × (1 − r₁/100) × (1 − r₂/100) × ...

Base Change in Percentages

Always identify the base of the percentage. If it says 'of the remaining', the previous balance becomes the new 100% for that specific step.

Shortcut Trick

Emma age = 45 − 25 = 20 years.

Sophia present age = 20 + 8 = 28 years.

Sophia age 7 years ago = 28 − 7 = 21 years (which is 7 units).

Ava age 7 years ago = 9 units = 27 years → Present age = 34 years.

50% of Ava present age = 34 ÷ 2 = 17 years.

∴ The correct answer is 17 years.

Alternate Method

Given: Ratio of Sophia and Ava (7 years ago) = 7 : 9. Emma age = Sophia − 8. Emma's father = 45 years and Emma + 25.

Formula: Age difference remains constant over time. Present age = Age (n years ago) + n.

⇒ Emma's father age = 45 years.

⇒ Emma's present age = 45 − 25 = 20 years.

⇒ Sophia's present age = 20 + 8 = 28 years.

⇒ Sophia's age 7 years ago = 28 − 7 = 21 years.

⇒ According to ratio 7 : 9, 7 units = 21 → 1 unit = 3.

⇒ Ava's age 7 years ago = 9 × 3 = 27 years.

⇒ Ava's present age = 27 + 7 = 34 years.

⇒ 50% of Ava's present age = 0.50 × 34 = 17 years.

∴ The correct answer is 17 years.

Additional Information

Age Ratio Concept

If the ratio of ages is a : b and n years pass, the new ratio is (ax+n) : (bx+n). The absolute difference between ages always remains constant.

Percentage Calculations

50% of a value is equivalent to dividing the value by 2 or multiplying by 1/2.

I. 2x² – 9x + 9 = 0

⇒ 2x² – 3x – 6x + 9 = 0

⇒ x (2x – 3) – 3 (2x – 3) = 0

⇒ (2x – 3) (x – 3) = 0

⇒ x = 3/2, 3

 

II. 2y² – 17y + 30 = 0

⇒ 2y² – 12y – 5y + 30 = 0

⇒ 2y (y – 6) – 5 (y – 6) = 0

⇒ (2y – 5) (y – 6) = 0

⇒ y = 5/2, 6

 

 

Hence, relationship between x and y cannot be established.

I. x² – 10x + 24 = 0

⇒ x² – 6x – 4x + 24 = 0

⇒ (x – 4) (x – 6) = 0

⇒ x =4, 6

II. 2y² – 29y + 105 = 0

⇒ 2y² – 15y – 14y + 105 = 0

⇒ (y – 7) (2y – 15) = 0

⇒ y = 7, 7.5  

 

 

Hence, x < y.

I. x² – 42x + 440 = 0

⇒ x² – 22x – 20x + 440 = 0

⇒ x(x – 22) – 20(x – 22) = 0

⇒ (x – 22) (x – 20) = 0

⇒ x = 22, 20

 

II. y² – 34y + 288 = 0

⇒ y² – 18y – 16y + 288 = 0

⇒ y(y – 18) – 16(y – 18) = 0

⇒ (y – 18) (y – 16) = 0

⇒ y = 18, 16

 

 

∴ x > y.

I. 25x² – 30x + 8 = 0

⇒ 25x² – 10x – 20x + 8 = 0

⇒ (5x – 4) (5x – 2) = 0

⇒ x =4/5, 2/5

II. 25y² – 50y + 24 = 0

⇒ 25y² – 20y – 30y + 24 = 0

⇒ (5y – 6) (5y – 4) = 0

⇒ y = 6/5, 4/5  

 

 

Hence, x ≤ y.

I. x² – 44x + 483 = 0

⇒ x² – 21x – 23x + 483 = 0

⇒ x (x – 21) – 23 (x – 21) = 0

⇒ (x – 21) (x – 23) = 0

⇒ x = 21, 23

 

II. y² – 27y + 182 = 0

⇒ y² – 14y – 13y + 182 = 0

⇒ y (y – 14) – 13 (y – 14) = 0

⇒ (y – 14) (y – 13) = 0

⇒ y = 14, 13

 

 

Hence x > y

Shortcut Trick

Side of cube (a) = ³√216 = 6 cm. Height of cuboid (h) = 6 cm.

Base area of cuboid = 480 ÷ 6 = 80 cm². Since ratio is 5 : 4, (5x) × (4x) = 80 ⇒ 20x² = 80 ⇒ x = 2.

Dimensions of cuboid: L = 10 cm, B = 8 cm, H = 6 cm.

Ratio = (6 × √3) : √(10² + 8² + 6²) = 6√3 : √200 = 6√3 : 10√2.

∴ The correct answer is 6√3 : 10√2.

Alternate Method

Given: Volume of cube = 216 cm³, Volume of cuboid = 480 cm³, L : B (cuboid) = 5 : 4, H (cuboid) = side of cube.

Formula Used: Volume of cube = a³, Diagonal of cube = a√3, Volume of cuboid = l × b × h, Diagonal of cuboid = √(l² + b² + h²).

⇒ a³ = 216 ⇒ a = 6 cm.

⇒ Height of cuboid (h) = 6 cm.

⇒ Let length (l) = 5x and breadth (b) = 4x.

⇒ 5x × 4x × 6 = 480 ⇒ 120x² = 480 ⇒ x² = 4 ⇒ x = 2.

⇒ l = 10 cm, b = 8 cm, h = 6 cm.

⇒ Diagonal of cube = 6√3 cm.

⇒ Diagonal of cuboid = √(10² + 8² + 6²) = √(100 + 64 + 36) = √200 = 10√2 cm.

⇒ Required Ratio = 6√3 : 10√2.

∴ The correct answer is 6√3 : 10√2.

Additional Information

Cube properties

Total Surface Area = 6a²; Lateral Surface Area = 4a².

Cuboid properties

Total Surface Area = 2(lb + bh + hl); Volume = lbh.

Diagonal length

The longest rod that can be placed inside a room is its space diagonal.

Shortcut Trick

Milk concentration in Container 1 = 3/7 and in Container 2 = 5/11.

Resultant Milk concentration = 4/9.

Using Alligation (Milk): |5/11 − 4/9| : |3/7 − 4/9| ⇒ 1/99 : 1/63 ⇒ 7 : 11.

Total ratio parts = 7 + 11 = 18 units = 18 L ∴ 1 unit = 1 L.

Quantity of 1^st mixture = 7 L. Milk in it = 7 × (3/7) = 3 L.

∴ The correct answer is 3 L.

Alternate Method

Given: Ratio 1 = 3:4, Ratio 2 = 5:6, Final Ratio = 4:5, Total Volume = 18 L.

Formula: Quantity₁ × (C₁ − C_m) = Quantity₂ × (C_m − C₂)

⇒ Let Q₁ and Q₂ be the volumes of the two containers.

⇒ Milk fraction: Q₁(3/7) + Q₂(5/11) = (Q₁ + Q₂)(4/9)

⇒ Q₁(4/9 − 3/7) = Q₂(5/11 − 4/9)

⇒ Q₁(1/63) = Q₂(1/99) ⇒ Q₁/Q₂ = 63/99 = 7/11

⇒ Total units = 7 + 11 = 18 → 18 L ∴ Q₁ = 7 L

⇒ Milk in 1^st container = 7 × (3 / (3 + 4)) = 7 × 3/7 = 3 L

∴ The correct answer is 3 L.

Additional Information

Alligation Rule

Used to find the ratio in which two ingredients at given prices/concentrations are mixed to produce a mixture of a mean price. Ratio = (Dearer − Mean) : (Mean − Cheaper).

Replacement Method

When a quantity is replaced repeatedly: Final Concentration = Initial Concentration × (1 − x/V)ⁿ, where x is replaced volume and V is total volume.

Multiple Mixtures

When mixing multiple containers, the total quantity of a component (milk) is the sum of quantities from each container: Σ(Ratio × Volume).

General Solution:

To find the value of x

100% = (x + 10)% + 60%

x = 30%

Number of orders received in company A = 450

Number orders packed in company A = 450 ×  (30 + 10)/100 = 180

Number of orders shipped in company A = (450 - 180) = 270

To find the value of y 

100% = (30% + y + 30%)

y = 40%

 

Company B:

Number of orders received in company  = 600

Number of orders packed in company  = 600 ×  (70/100) = 420

Number of orders shipped in company  = (600 - 420) = 180

 

Company C:

Number of orders received in company  = 700

Number of orders packed in company  = 700 ×  (60 - 5)/100)) = 385

Number of orders shipped in company  = (700 - 385) = 315

 

Company D:

Number of orders received in company  = 2650 - (450 + 600 + 700 + 400) = 500

Number of orders packed in company  = 500 ×  (65/100) = 325

Number of orders shipped in company  = (500 - 325) = 175

 

Company E:

Number of orders received in company  = 400

Number of orders shipped in company  = 400 ×  25/100 = 100

Number of orders packed in company  = (400 - 100) = 300

 

Solution:

Number of international orders packed in company E = 300/5 = 60

Number of national orders packed in company E = (300 - 60) = 240

Number of international shipped in company B = 180/3 = 60

Number of national orders shipped in company B = (180 - 60) = 120

Required sum = (240/3 + 120 ×  2/3) = 160

General Solution:

To find the value of x

100% = (x + 10)% + 60%

x = 30%

Number of orders received in company A = 450

Number orders packed in company A = 450 ×  (30 + 10)/100 = 180

Number of orders shipped in company A = (450 - 180) = 270

To find the value of y 

100% = (30% + y + 30%)

y = 40%

 

Company B:

Number of orders received in company  = 600

Number of orders packed in company  = 600 ×  (70/100) = 420

Number of orders shipped in company  = (600 - 420) = 180

 

Company C:

Number of orders received in company  = 700

Number of orders packed in company  = 700 ×  (60 - 5)/100)) = 385

Number of orders shipped in company  = (700 - 385) = 315

 

Company D:

Number of orders received in company  = 2650 - (450 + 600 + 700 + 400) = 500

Number of orders packed in company  = 500 ×  (65/100) = 325

Number of orders shipped in company  = (500 - 325) = 175

 

Company E:

Number of orders received in company  = 400

Number of orders shipped in company  = 400 ×  25/100 = 100

Number of orders packed in company  = (400 - 100) = 300

 

Solution:

Number orders packed in company A = 180

Number of orders shipped in company A = 270 

Cost for packing each orders = Rs. 15

Cost for shipping each orders = Rs. 30

Total amount = (180 ×  1/5 ×  15 + 270 ×  2/3 ×  30) = (540 + 5400) = (5940)

General Solution:

To find the value of x

100% = (x + 10)% + 60%

x = 30%

Number of orders received in company A = 450

Number orders packed in company A = 450 ×  (30 + 10)/100 = 180

Number of orders shipped in company A = (450 - 180) = 270

To find the value of y 

100% = (30% + y + 30%)

y = 40%

 

Company B:

Number of orders received in company  = 600

Number of orders packed in company  = 600 ×  (70/100) = 420

Number of orders shipped in company  = (600 - 420) = 180

 

Company C:

Number of orders received in company  = 700

Number of orders packed in company  = 700 ×  (60 - 5)/100)) = 385

Number of orders shipped in company  = (700 - 385) = 315

 

Company D:

Number of orders received in company  = 2650 - (450 + 600 + 700 + 400) = 500

Number of orders packed in company  = 500 ×  (65/100) = 325

Number of orders shipped in company  = (500 - 325) = 175

 

Company E:

Number of orders received in company  = 400

Number of orders shipped in company  = 400 ×  25/100 = 100

Number of orders packed in company  = (400 - 100) = 300

 

Solution:

Number of orders packed in company A = 180

Number of orders packed in company E = 300

Number of orders shipped in company A = 270

Number of orders shipped in company E = 100

Required ratio = (180 + 300): (270 + 100) = (480: 370) = 48: 37

General Solution:

To find the value of x

100% = (x + 10)% + 60%

x = 30%

Number of orders received in company A = 450

Number orders packed in company A = 450 ×  (30 + 10)/100 = 180

Number of orders shipped in company A = (450 - 180) = 270

To find the value of y 

100% = (30% + y + 30%)

y = 40%

 

Company B:

Number of orders received in company  = 600

Number of orders packed in company  = 600 ×  (70/100) = 420

Number of orders shipped in company  = (600 - 420) = 180

 

Company C:

Number of orders received in company  = 700

Number of orders packed in company  = 700 ×  (60 - 5)/100)) = 385

Number of orders shipped in company  = (700 - 385) = 315

 

Company D:

Number of orders received in company  = 2650 - (450 + 600 + 700 + 400) = 500

Number of orders packed in company  = 500 ×  (65/100) = 325

Number of orders shipped in company  = (500 - 325) = 175

 

Company E:

Number of orders received in company  = 400

Number of orders shipped in company  = 400 ×  25/100 = 100

Number of orders packed in company  = (400 - 100) = 300

 

Solution:

Number of orders packed in company D = 325

Number orders shipped in company D = 175

If number of orders packed increased by 20% and number of orders shipped increased by x%, 

325 ×  120/100 = 390

Total orders packed and shipped after increased = 635

635 - 390 = 245

To find the value of x

x = (245 - 175)/175 ×  100 = 70/175 ×  100 = 40%

General Solution:

To find the value of x

100% = (x + 10)% + 60%

x = 30%

Number of orders received in company A = 450

Number orders packed in company A = 450 ×  (30 + 10)/100 = 180

Number of orders shipped in company A = (450 - 180) = 270

To find the value of y 

100% = (30% + y + 30%)

y = 40%

 

Company B:

Number of orders received in company  = 600

Number of orders packed in company  = 600 ×  (70/100) = 420

Number of orders shipped in company  = (600 - 420) = 180

 

Company C:

Number of orders received in company  = 700

Number of orders packed in company  = 700 ×  (60 - 5)/100)) = 385

Number of orders shipped in company  = (700 - 385) = 315

 

Company D:

Number of orders received in company  = 2650 - (450 + 600 + 700 + 400) = 500

Number of orders packed in company  = 500 ×  (65/100) = 325

Number of orders shipped in company  = (500 - 325) = 175

 

Company E:

Number of orders received in company  = 400

Number of orders shipped in company  = 400 ×  25/100 = 100

Number of orders packed in company  = (400 - 100) = 300

 

Solution:

Number of orders packed in company D = 325

Number of orders packed in company F = (325 + 25) = 350

Number of orders shipped in company B = 180

Number of orders shipped in company F = (180 + 20) = 200

Required difference = (350 - 200) = 150

Shortcut Trick

Let the shares be A = 7k, B = 13k, and C = 17k.

x = (2/3) × A, y = (1/2) × B, z = (1/3) × C.

x : y : z = (2/3 × 7) : (1/2 × 13) : (1/3 × 17) = 14/3 : 13/2 : 17/3.

Multiply by LCM 6 → 28 : 39 : 34.

∴ The correct answer is 28 : 39 : 34.

Alternate Method

Given: Ratio of A : B : C = 7 : 13 : 17

Calculations:

⇒ A = 7k, B = 13k, C = 17k

⇒ x = A − (1/3)A = (2/3)A = (2/3) × 7k = 14k/3

⇒ y = B − (1/2)B = (1/2)B = (1/2) × 13k = 13k/2

⇒ z = C − (2/3)C = (1/3)C = (1/3) × 17k = 17k/3

⇒ x : y : z = (14/3) : (13/2) : (17/3)

⇒ Multiply by LCM(2, 3) = 6: (14/3 × 6) : (13/2 × 6) : (17/3 × 6)

⇒ x : y : z = 28 : 39 : 34

∴ The correct answer is 28 : 39 : 34.

Additional Information

Ratio and Proportion

To simplify fractional ratios, multiply each term by the LCM of all denominators to obtain an integer ratio.

Compound Ratio

The compound ratio of (a : b) and (c : d) is (ac : bd), used when multiple ratios interact in a product form.

Shortcut Trick

Profit of Ram = 1000 × (x ÷ 100) = 10x.

Net profit % of Shyam = 2x − x − (2x × x ÷ 100) = x − (x² ÷ 50).

Profit of Shyam = 2000 × [x − (x² ÷ 50)] ÷ 100 = 20x − 0.4x².

Equating profits: 10x = 20x − 0.4x² ⇒ 0.4x² = 10x ⇒ 0.4x = 10.

x = 10 ÷ 0.4 = 25.

∴ The correct answer is 25%.

Alternate Method

Given: CP_Ram = Rs. 1000, CP_Shyam = Rs. 2000. Ram markup = x%. Shyam markup = 2x%, Discount = x%.

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

⇒ Profit of Ram = 1000 × (x ÷ 100) = 10x.

⇒ Selling Price of Shyam = 2000 × (100 + 2x) ÷ 100 × (100 − x) ÷ 100.

⇒ SP_Shyam = 2000 × (10000 − 100x + 200x − 2x²) ÷ 10000 = (10000 + 100x − 2x²) ÷ 5 = 2000 + 20x − 0.4x².

⇒ Profit of Shyam = SP − CP = (2000 + 20x − 0.4x²) − 2000 = 20x − 0.4x².

⇒ Since Profits are equal: 10x = 20x − 0.4x².

⇒ 0.4x² − 10x = 0 ⇒ x(0.4x − 10) = 0.

⇒ x = 10 ÷ 0.4 = 25.

∴ The correct answer is 25%.

Additional Information

Marked Price and Markup

Markup is the amount added to the Cost Price to arrive at the Marked Price. Markup% = (Markup ÷ CP) × 100.

Successive Percentage Change

When an item is marked up by a% and then a discount of b% is given, the net profit% is given by the formula: a − b − (ab ÷ 100).

In the number series 8, 17, 35, 71, 145, 287, 575

We observe the relation

8 × 2 + 1 = 17

17 × 2 + 1 = 35

35 × 2 + 1 = 71

71 × 2 + 1 = 143   (wrong)

143 × 2 + 1 = 287

287 × 2 + 1 = 575

Thus, we get that 145 is the wrong number in the series

In the above series 210, 206, 197, 181, 156, 121, 71

210 - 2² = 206

206 - 3² = 197

197 - 4² = 181

181 - 5² =  156

156 - 6² = 120

120 - 7² = 71 

Thus, 121 is the wrong number.

The series follows the following pattern

⇒ 3 × 1 + 1 = 4

⇒ 4 × 1.5 – 1.5 = 4.5

⇒ 4.5 × 2 + 2 = 11

⇒ 11 × 2.5 – 2.5 = 25

⇒ 25 × 3 + 3 = 78

⇒ 78 × 3.5 – 3.5 = 269.5

∴ The wrong number in the series is 80.

16 × 1 + 1² = 17

17 × 2 + 2² = 38

38 × 3 + 3² = 123

123 × 4 + 4² = 508

508 × 5 + 5² = 2565

∴ Wrong term in given number series is 510.

6 + 1³ = 7

7 + 2² = 11

11 + 3³ = 38

38 + 4² = 54

54 + 5³ = 179

179 + 6² = 215

∴ Wrong number in given number series is 214.

Shortcut Trick

For 2 years, the difference between CI and SI is given by: D = P × (r/100)².

⇒ 72 = 5000 × (x/100)²

⇒ 72 = 5000 × (x² / 10000)

⇒ 72 = x² / 2 ⇒ x² = 144 ⇒ x = 12%.

∴ The correct answer is 12%.

Alternate Method

Given: Principal (P) = ₹5000, Time (T) = 2 years, Difference (D) = ₹72.

Formula Used: Difference (D) = P(r/100)²

⇒ 72 = 5000 × (x/100) × (x/100)

⇒ 72 = 5000 × x² / 10000

⇒ 72 = x² / 2

⇒ x² = 72 × 2 = 144

⇒ x = √144 = 12

∴ The correct answer is 12%.

Additional Information

CI and SI Difference for 3 years

The formula for the difference between CI and SI for 3 years is D = P(r/100)² × (3 + r/100).

Effective Rate Method

For 2 years, effective SI rate is 2r% and effective CI rate is (2r + r²/100)%. The difference is always (r²/100)% of Principal.

Shortcut Trick

Let Upstream speed be U and Downstream speed be D.

Ratio of distances D : U = 60 : 40 = 3 : 2 (Time is constant, so speed ratio = distance ratio).

Given: 10/U + 10/D = 25/12 ⇒ 10/(2x) + 10/(3x) = 25/12 ⇒ (15 + 10)/3x = 25/12 ⇒ 25/3x = 25/12 ⇒ x = 4.

So, U = 8 kmph and D = 12 kmph.

Required Time = 24/8 + 24/12 = 3 + 2 = 5 hours.

∴ The correct answer is 5 hr.

Alternate Method

Given:

⇒ Time for 40 km Upstream = Time for 60 km Downstream

⇒ 40/U = 60/D ⇒ D = 1.5U

Condition 2:

⇒ 10/U + 10/D = 25/12 hours

⇒ 10/U + 10/(1.5U) = 25/12

⇒ 10/U + 20/(3U) = 25/12

⇒ (30 + 20) / 3U = 25/12

⇒ 50 / 3U = 25/12 ⇒ 2/U = 1/4 ⇒ U = 8 kmph

⇒ D = 1.5 × 8 = 12 kmph

Final Calculation:

⇒ Required Time = 24/U + 24/D

⇒ Time = 24/8 + 24/12 = 3 + 2 = 5 hr

∴ The correct answer is 5 hr.

Additional Information

Upstream and Downstream Speed

Downstream Speed (D) = Speed of boat (u) + Speed of stream (v); Upstream Speed (U) = Speed of boat (u) − Speed of stream (v).

Boat Speed in Still Water

Speed of boat in still water (u) = (D + U) ÷ 2.

Speed of Stream

Speed of the current/stream (v) = (D − U) ÷ 2.

Shortcut Trick

Amit: 10 questions × ₹70 × 2 weeks = ₹1400

Vishal: (2 questions/day × 7 days) × ₹80 × 2 weeks = ₹2240

Total: ₹1400 + ₹2240 = ₹3640

∴ The correct answer is ₹3640.

Alternate Method

Given:

Questions by Amit per week = 10; Rate = ₹70/question

Questions by Vishal per day = 2; Rate = ₹80/question

Time period = 2 weeks (14 days)

Calculations:

⇒ Total questions by Amit in 2 weeks = 10 × 2 = 20 questions

⇒ Amount for Amit = 20 × 70 = ₹1400

⇒ Total questions by Vishal in 2 weeks = 2 × 14 = 28 questions

⇒ Amount for Vishal = 28 × 80 = ₹2240

⇒ Total amount = 1400 + 2240 = ₹3640

∴ The correct answer is ₹3640.

Additional Information

Unitary Method

Total Earning = (Quantity of Work done per unit time × Total Time) × Rate per unit of work.

Time Conversion

Always ensure the time units are consistent (e.g., converting weeks to days if the rate is given per day). 1 standard week = 7 days.

Shortcut Trick

From Statement I: 40% of Females = 120 ⇒ Total Females = 300.

From Statement II: Total Females (300) = 1.25 × (60% of Males).

300 = 1.25 × 0.6 × Males ⇒ 300 = 0.75 × Males ⇒ Total Males = 400.

Average = (300 + 400) ÷ 2 = 350. Both statements are required.

∴ The correct answer is 350.

Alternate Method

Given: Participated Males = 60% of M; Participated Females = 40% of F.

From Statement I:

⇒ 40% of F = 120

⇒ F = (120 × 100) ÷ 40 = 300

⇒ Total Females = 300. (M is unknown, only M > 300 is given).

From Statement II:

⇒ F = 125% of (Participated Males)

⇒ F = 1.25 × (60% of M)

Combining I and II:

⇒ 300 = 1.25 × 0.60 × M

⇒ 300 = 0.75 × M

⇒ M = 300 ÷ 0.75 = 400

⇒ Average = (300 + 400) ÷ 2 = 350

∴ The correct answer is 350.

Additional Information

Data Sufficiency approach

Always check if a unique value can be determined. If two variables (M and F) are present, you generally need two independent linear equations.

Percentage to Fraction Conversion

25% more means a multiplier of 1.25 or 5/4. 60% means 3/5 and 40% means 2/5.

Average Formula

The average of two quantities A and B is calculated as (A + B) ÷ 2.

Number = 10x + y

From statement I:

(10x + y) – (10y + x) = 18

⇒ x – y = 2     ----(i)

From statement II:

x + y = 8     ----(ii)

From statement III:

x – y = 2      ----(iii)

By the help of equation (i) or (iii) and (ii)

⇒ x = 5 and y = 3

Number = 53

∴ Either statement I or statement III is not necessary to answer the question

Calculation:

From statement I

Ratio of efficiency of A and C is 5 : 9

Ratio of time taken by A and C is 9 : 5

A takes 8 days more than C to finish the work

⇒ (9 – 5) units = 8 days

⇒ 4 units = 8 days

⇒ 1 unit = 2 days

∴ A will complete the work in = 9 × 2 = 18 days

From statement II

A and B working together can complete the work in 10 days

⇒ 1/A + 1/B = 1/10

C is twice efficient than A

∴ The data in statement I alone is sufficient to answer the question, while the data in II alone is not sufficient to answer the question.

Formula used:

Length of a train = Speed of the train × time taken to cross a pole

Length of a train = Relative Speed (S_t + S_m) × Time taken to cross a man

Calculation:

Let the Length of the Train A be L_t

Statement I

Speed of a train (S_t) = x m/s

Speed of a man (S_m) = 10 m/s

Time Taken = 10 sec

Length of the Train A (L_t) = Relative Speed (S_t + S_m) × Time taken to cross a man

Length of the Train A (L_t) = (x + 10) × 10

As you can see Speed of the train is needed to find the answer, let’s check the other statement

Statement II

Speed of Train B = 2 × Speed of Train A

Speed of Train B = 2x

Time Taken to cross a Pole = 5 sec

Length of Train B = 500 m

Length of the Train = Speed of Train × Time taken to cross a pole

500 = 2x × 5

x = 500/10

x = 50 m/s

From Statement II, we get the Speed of  Train A, and put it in statement I

Length of Train A (L_t) = (50 + 10) × 10 = 60 × 10

Length of Train A (L_t) = 600 m

∴ Statement I and II together are necessary to answer the questions.

Shortcut Trick

In an Arithmetic Progression (AP), the Average is always the mean of the first term and the last term.

Average = (Lightest + Heaviest) ÷ 2

33 = (5 + x) ÷ 2

66 = 5 + x ⇒ x = 61

∴ The correct answer is 61.

Alternate Method

Given: Average weight = 33 kg, Number of people = x, Lightest weight (a) = 5 kg, Heaviest weight (l) = x kg.

Formula Used: Sum of AP (S_n) = (n ÷ 2) × (a + l); Average = Sum ÷ n

⇒ Average = [(x ÷ 2) × (5 + x)] ÷ x

⇒ 33 = (5 + x) ÷ 2

⇒ 66 = 5 + x

⇒ x = 66 − 5

⇒ x = 61

∴ The correct answer is 61.

Additional Information

Properties of AP Average

For any Arithmetic Progression, the Average is equivalent to the middle term (if n is odd) or the mean of the two middle terms (if n is even).

Sum of n terms in AP

S_n = n/2 × [2a + (n−1)d], where a is the first term, d is the common difference, and n is the number of terms.

Shortcut Trick

Total profit in the first year = Rs. 10000, and in the second year = Rs. 8044.44.

Total profit for both years combined = 10000 + 8044.44 = Rs. 18044.44.

For each year, 5% is allocated to Charity, and 5% is added equally to their investments (2.5% each). The remaining 90% is divided in the investment ratio.

Since the initial investment ratio is 70000 : 20000 = 7 : 2, and the 5% addition is equal (2.5% of total profit each), A receives his share from the 2.5% equal distribution plus his proportion of the 90% remaining profit.

In the first year, investment is in the ratio 7 : 2. After adding 5% of profit (Rs. 500 equally, i.e., Rs. 250 each), the new investments for the second year become Rs. 70250 and Rs. 20250, which is approximately the same ratio (70.25 : 20.25 ≈ 7 : 2).

A's total share ≈ 2.5% of Total Profit + 7/9 × 90% of Total Profit = 2.5% + 70% = 72.5% of the total profit.

Total Profit of A ≈ 72.5% of 18044.44 ≈ Rs. 12620.

∴ The correct answer is Rs. 12620.

Alternate Method

Given:

Initial capital of A = Rs. 70000, Initial capital of B = Rs. 20000

First year profit = Rs. 10000, Second year profit = Rs. 8044.44

Formulas:

Profit Distribution = Charity (5%) + Equal addition to investment (5%) + Remaining profit distributed in investment ratio (90%)

Step-by-step Solution:

⇒ First Year Profit Distribution:

⇒ Total profit = Rs. 10000

⇒ Charity (5%) = Rs. 500

⇒ Added to Investment (5%) = Rs. 500 (Rs. 250 each to A and B)

⇒ Remaining profit (90%) = Rs. 9000. Divided in the ratio of initial investments (70000 : 20000 = 7 : 2).

⇒ A's share from remaining profit = 9000 × (7 ÷ 9) = Rs. 7000

⇒ Total profit received by A in the 1^st year = Rs. 250 (equal addition) + Rs. 7000 = Rs. 7250

⇒ New Investments at the start of the 2^nd year: A = 70000 + 250 = Rs. 70250, B = 20000 + 250 = Rs. 20250

⇒ Second Year Profit Distribution:

⇒ Total profit = Rs. 8044.44

⇒ Added to Investment (5%) = 5% of 8044.44 = Rs. 402.22 (Rs. 201.11 each to A and B)

⇒ Remaining profit (90%) = 90% of 8044.44 = Rs. 7240

⇒ Remaining profit divided in the new investment ratio (70250 : 20250 = 281 : 81). Sum of ratio parts = 281 + 81 = 362.

⇒ A's share from remaining profit = 7240 × (281 ÷ 362) = 20 × 281 = Rs. 5620

⇒ Total profit received by A in the 2^nd year = Rs. 201.11 + Rs. 5620 = Rs. 5821.11

⇒ Total Profit of A:

⇒ Total Profit of A = Profit of 1^st Year + Profit of 2^nd Year = 7250 + 5821.11 ≈ Rs. 13071.11 (without considering equal addition as part of personal withdrawal profit) or if the 5% added to investment is considered part of the total profit accumulated by A: 7250 + 5821.11 ≈ 13071.11. Let's recalculate if the 5% added to investment is NOT accumulated as profit payout, but only the 90% remaining is distributed: 1^st Year = 7000, 2^nd Year = 5620. Total = 7000 + 5620 = 12620.

⇒ In business partnership questions, the portion reinvested is part of capital and the distributed profit is from the 90% split, plus potentially the 5% equal addition. If only the remaining profit is distributed, A's profit = 7000 + 5620 = Rs. 12620.

∴ The correct answer is Rs. 12620.

Additional Information

Partnership Profit Distribution

In a partnership, unless specified otherwise, profits are distributed in the ratio of the product of the capital invested and the time period of investment: Profit Ratio = (C₁ × T₁) : (C₂ × T₂).

1) Nina likes Minecraft and not more than two persons are sitting to the left of Nina. One person sits between Nina and Hema. 

2) The number of persons sitting between Rani and Keshav is one less than the number of persons sitting to the right of Hema. Keshav and the person who like Pubg are not sitting at the extreme end. The person who likes Pubg is sitting to the immediate right of Keshav. 

Cases 1 and 2 cannot satisfy the given conditions. That is why, Cases 1 and 2 are eliminated.

3) The person who likes Duty is sitting immediately right of Sam. This condition is not satisfied in Case 3(b). That is why Case 3(b) is eliminated.

4) Two persons sit between the person who likes Combat and Duty. The person who likes Free Fire is not an immediate neighbor of the one who likes Duty. This condition is not satisfied in Case 4. That is why Case 4 is eliminated.

The final arrangement is:

Two persons are sitting between Hema and the person who likes Free fire. Hence, Hema is an immediate neighbor of the one who likes Free fire is not true.

1) Nina likes Minecraft and not more than two persons are sitting to the left of Nina. One person sits between Nina and Hema. 

2) The number of persons sitting between Rani and Keshav is one less than the number of persons sitting to the right of Hema. Keshav and the person who like Pubg are not sitting at the extreme end. The person who likes Pubg is sitting to the immediate right of Keshav. 

Cases 1 and 2 cannot satisfy the given conditions. That is why, Cases 1 and 2 are eliminated.

3) The person who likes Duty is sitting immediately right of Sam. This condition is not satisfied in Case 3(b). That is why Case 3(b) is eliminated.

4) Two persons sit between the person who likes Combat and Duty. The person who likes Free Fire is not an immediate neighbor of the one who likes Duty. This condition is not satisfied in Case 4. That is why Case 4 is eliminated.

The final arrangement is:

Keshav likes Combat. Hence, Keshav-Combat is the correct combination.

1) Nina likes Minecraft and not more than two persons are sitting to the left of Nina. One person sits between Nina and Hema. 

2) The number of persons sitting between Rani and Keshav is one less than the number of persons sitting to the right of Hema. Keshav and the person who like Pubg are not sitting at the extreme end. The person who likes Pubg is sitting to the immediate right of Keshav. 

Cases 1 and 2 cannot satisfy the given conditions. That is why, Cases 1 and 2 are eliminated.

3) The person who likes Duty is sitting immediately right of Sam. This condition is not satisfied in Case 3(b). That is why Case 3(b) is eliminated.

4) Two persons sit between the person who likes Combat and Duty. The person who likes Free Fire is not an immediate neighbor of the one who likes Duty. This condition is not satisfied in Case 4. That is why Case 4 is eliminated.

The final arrangement is:

if Rani takes the place of Keshav, Keshav takes place of Tabu and Tabu takes place of Rani, the rearrangement is:

Hence, Rani is immediately right of the person who likes Minecraft.

1) Nina likes Minecraft and not more than two persons are sitting to the left of Nina. One person sits between Nina and Hema. 

2) The number of persons sitting between Rani and Keshav is one less than the number of persons sitting to the right of Hema. Keshav and the person who like Pubg are not sitting at the extreme end. The person who likes Pubg is sitting to the immediate right of Keshav. 

Cases 1 and 2 cannot satisfy the given conditions. That is why, Cases 1 and 2 are eliminated.

3) The person who likes Duty is sitting immediately right of Sam. This condition is not satisfied in Case 3(b). That is why Case 3(b) is eliminated.

4) Two persons sit between the person who likes Combat and Duty. The person who likes Free Fire is not an immediate neighbor of the one who likes Duty. This condition is not satisfied in Case 4. That is why Case 4 is eliminated.

The final arrangement is:

Hence, Four persons are sitting between the one who likes Duty and Rani.

1) Nina likes Minecraft and not more than two persons are sitting to the left of Nina. One person sits between Nina and Hema. 

2) The number of persons sitting between Rani and Keshav is one less than the number of persons sitting to the right of Hema. Keshav and the person who like Pubg are not sitting at the extreme end. The person who likes Pubg is sitting to the immediate right of Keshav. 

Cases 1 and 2 cannot satisfy the given conditions. That is why, Cases 1 and 2 are eliminated.

3) The person who likes Duty is sitting immediately right of Sam. This condition is not satisfied in Case 3(b). That is why Case 3(b) is eliminated.

4) Two persons sit between the person who likes Combat and Duty. The person who likes Free Fire is not an immediate neighbor of the one who likes Duty. This condition is not satisfied in Case 4. That is why Case 4 is eliminated.

The final arrangement is:

Hence, Hema sits immediately to the right of the person who likes Combat.