IBPS PO Prelims Memory Based Paper (Held On: 30 September 2023 Shift 1) (Previous Year Paper)

The correct answer is option 2), i.e., Soothing.​

Explanation 

The meaning of both words are:

Disconcerting: causing one to feel unsettled. Soothing: assuasive or calming.

Additional Information

The meanings of other words:

• Perturbing: make (someone) anxious or unsettled.
• Efficacious: (of something inanimate or abstract) successful in producing a desired or intended result; effective.
• Tenacious: tending to keep a firm hold of something; clinging or adhering closely.
• Fastidious: very attentive to and concerned about accuracy and detail.

​As you can see, of all the options, 'Assuasive' is the most opposite in meaning to the world 'Disconcerting'.

The correct answer is option 4), i.e., The rejection of the proposition that climate change caused by human activity is occurring.

Explanation 

• Climate change denial is denial, dismissal, or unwarranted doubt that contradicts the scientific agreement on climate change, including the extent to which it is caused by humans, its effects on nature and human society.
• Option 3 is the opposite of what 'climate denial' means. 'Climate denial' is the claim that climate change is not happening and that climate scientists are lying and their data is fake.
• Option 1 and option 2 do not make sense here.

Thus, option 4) is the correct answer.

The correct answer is option 2), i.e., Global warming makes us realise that if we wish to survive on this planet, we need to be considerate and keep track of the activities that may be harmful to the environment.

Explanation  Global warming counsels human humility as its presence shows that we cannot just do whatever we want. We need to be watchful of what we do. We cannot just go on polluting the environment with greenhouse gases and expect that they will not have any adverse effect.

The correct answer is option 4), i.e., Pessimism Regarding Climate Change.

Explanation 

• The author is listing the reasons why we must take responsibility for climate change.
• He is also quoting facts such as wildfires in California, hurricanes frequency, the collapse of ice sheets, etc.
• The line 'no matter how hot it gets, no matter how fully climate change transforms the planet and the way we live on it, it will always be the case that the next decade could contain more warming' shows the author's pessimism (and rightly so) regarding climate change.

The correct answer is option 5), i.e., Conventional.​

Explanation 

The meanings of both words are:

Unprecedented: never done or known before. Conventional: based on or following what is generally done or believed.

Additional Information

The meanings of other words:

• Incendiary: (of a device or attack) designed to cause fires.
• Egregious: outstandingly bad; shocking.
• Extraordinary: very unusual or remarkable. Intransigent: unwilling or refusing to change one's views or to agree about something.

As you can see, of all the options, 'Conventional' is the most opposite in meaning to the word 'Unprecedented'.

The correct answer is option 5), i.e., The problem of global warming gets worse over time, the longer we produce greenhouse gas, and no matter how hot it gets, the next decade could be even warmer.

 

Explanation 

• It is mentioned in the passage that global warming is a problem that gets worse over time, the longer we produce greenhouse gas. It is also mentioned that no matter how hot it gets, the next decade 'could contain more warming'.
• The predictions regarding the global temperature, sea-level, hurricane frequency and wildfire volume can appear false, but they are not false.
• The clouds of uncertainty regarding climate change do not show our collective ignorance, however, they show us our blindness towards the human world.
• ​The scientists know a great deal about climate change, although there is still a lot to learn as there are mechanisms related to the climate system that are not yet fully understood.

The correct answer is option 5), i.e., All of the above.

Explanation 

• ​It is explicitly mentioned in the passage that if the temperature increases just 'one degree north of where we are today', some of the planet's ice sheets are expected to begin their collapse, which will raise the sea level by as much as 50 feet.
• Again, it is given in the passage that wildfires have burned through 1.6 million acres of land in California.
• The last line mentions how major cities in the equatorial band of the planet will become unlivable, and it is implied (as already given in the last line) that it will be due to the rise in sea level resulting from the collapse of ice sheets.
• The author has mentioned that climate change is 'all-enveloping means that it targets us all.'

The correct answer is option 4), i.e., Cautionary.

Explanation  The author is quoting examples (like wildfires and the assertion that major cities will become unlivable) that seem to be serving as a warning. He is also letting us know that the problems of climate change affect us all. Moreover, he is also appealing to us that 'we must share in the responsibility, so we do not share in the suffering.'

Additional Information

• Cautionary - serving as a warning.
• Acerbic - sharply or bitingly critical, sarcastic, or ironic in temper, mood, or tone.
• Speculative -  involving, based on, or constituting intellectual speculation; theoretical rather than practical.
• Introspective - this is the tone when the author is indulging in self-examination, and reflecting upon one’s actions and feelings
• Optimistic - hopeful and confident about the future.

The correct answer is C-D.

Key Points

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

____ (A) and thousands of ____ (B) were switchboard ____ (C) before direct dial ____ (D) were in use.

• 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
• operators refer to the mentioned women.
• So, C and D should be interchanged to make the sentence correct.

Therefore the correct sentence is - Thousands and thousands of women were switchboard operators before direct dial phones were in use.

The correct answer is B-C.

Key Points

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

For ____ (A) years the industry was ____ (B), but was ____ (C) on a ____ (D) scale in 1903.

• 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
• but was  abandoned on a small scale in 1903. is incorrect in meaning. Nothing can be 'abandoned' on a small scale.
• 'abandoned' is best interchanged with restarted to make the sentence correct.

Therefore the correct sentence is - For some years the industry was abandoned, but was restarted on a small scale in 1903.​

The correct answer is A-C.

Key Points

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

After ____ (A) the ____ (B), he restarted his ____ (C) career on the west coast with ____ (D) and television roles.

• 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
• After  entertainment  maybe a correct phrase but it does not fit the context of the sentence.
• he restarted his leaving career  is an incorrect phrase.
• So, A and C should be interchanged to make the sentence correct.

Therefore the correct sentence is - After leaving the army, he restarted his entertainment career on the west coast with movie and television roles.

Hint

• To maintain continuity the indefinite pronoun 'someone' should be followed by another indefinite pronoun.
• Hence, anyone should come after someone.

The correct answer is B-D.

Key Points

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

He ____ (A) to have ____ (B) over the incident, ____ (C) our concerns over his ____ (D) mental wellbeing.

• 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
• to have fragile  is an incorrect phrase.
• his nightmares mental wellbeing is also incorrect.
• So, B and D should be interchanged to make the sentence correct.

Therefore the correct sentence is - He continued to have nightmares over the incident, renewing our concerns over his fragile mental wellbeing.

Hint

• Although the question is based on vocabulary knowledge, grammatical rules can be applied to solve it.
• 'fragile'  is an adjective while 'nightmares' is a noun.
• Hence, fragile is best suited to describe the phrase 'mental wellbeing'.

The correct answer is A-B.

Key Points

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

The ____ (A) done to half her face caused ____ (B) scarring that left her features ____ (C) and her skin ____ (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 horrible (A) done to half her face caused damage (B) scarring is incorrect
• So, A and B should be interchanged to make the sentence correct.

Therefore the correct sentence is - The damage done to half her face caused horrible scarring that left her features lopsided and her skin knotted.

Hint

• Although the question is based on vocabulary knowledge, grammatical rules can be applied to solve it.
• 'horrible'  is an adjective and is best suited to describe the gerund 'scarring'.

The correct answer is option 1 i.e. A

Key Points

• ‘A’ is the only sentence which can be used as the opening sentence as the use of words "Hence, But Therefore etc." in other sentences points that they must be used in between other sentences. So, A is the first statement.
• ‘E’ is in direct contrast to ‘A’ as it tries to answer what’s asked in ‘A’. So, E is the second statement.
• ‘F’ is next as it supplements the information given in ‘E’ i.e. even though we have knowledge and capacity to store we need training to be efficient. So, F is the third statement.
• ‘C’ and ‘D’ are linked and must be used together in that order. C introduces two aspects educated and uneducated and D says what they can do. So, C is the fourth statement and D is the fifth statement.
• ‘B’ is the ideal choice for closing the passage as it provides a conclusion of what’s discussed earlier. So, B is the last statement.

The correct order A-E-F-C-D-B.

Thus the first sentence is A.

The correct answer is option 5 i.e. E

Key Points

• ‘A’ is the only sentence which can be used as the opening sentence as the use of words "Hence, But Therefore etc." in other sentences points that they must be used in between other sentences. So, A is the first statement.
• ‘E’ is in direct contrast to ‘A’ as it tries to answer what’s asked in ‘A’. So, E is the second statement.
• ‘F’ is next as it supplements the information given in ‘E’ i.e. even though we have knowledge and capacity to store we need training to be efficient. So, F is the third statement.
• ‘C’ and ‘D’ are linked and must be used together in that order. C introduces two aspects educated and uneducated and D says what they can do. So, C is the fourth statement and D is the fifth statement.
• ‘B’ is the ideal choice for closing the passage as it provides a conclusion of what’s discussed earlier. So, B is the last statement.

The correct order A-E-F-C-D-B.

Thus the second sentence is E.

The correct answer is option 3 i.e. C

Key Points

• ‘A’ is the only sentence which can be used as the opening sentence as the use of words "Hence, But Therefore etc." in other sentences points that they must be used in between other sentences. So, A is the first statement.
• ‘E’ is in direct contrast to ‘A’ as it tries to answer what’s asked in ‘A’. So, E is the second statement.
• ‘F’ is next as it supplements the information given in ‘E’ i.e. even though we have knowledge and capacity to store we need training to be efficient. So, F is the third statement.
• ‘C’ and ‘D’ are linked and must be used together in that order. C introduces two aspects educated and uneducated and D says what they can do. So, C is the fourth statement and D is the fifth statement.
• ‘B’ is the ideal choice for closing the passage as it provides a conclusion of what’s discussed earlier. So, B is the last statement.

The correct order A-E-F-C-D-B.

Thus the fourth sentence is C.

The correct answer is option 5 i.e. D

Key Points

• ‘A’ is the only sentence which can be used as the opening sentence as the use of words "Hence, But Therefore etc." in other sentences points that they must be used in between other sentences. So, A is the first statement.
• ‘E’ is in direct contrast to ‘A’ as it tries to answer what’s asked in ‘A’. So, E is the second statement.
• ‘F’ is next as it supplements the information given in ‘E’ i.e. even though we have knowledge and capacity to store we need training to be efficient. So, F is the third statement.
• ‘C’ and ‘D’ are linked and must be used together in that order. C introduces two aspects educated and uneducated and D says what they can do. So, C is the fourth statement and D is the fifth statement.
• ‘B’ is the ideal choice for closing the passage as it provides a conclusion of what’s discussed earlier. So, B is the last statement.

The correct order A-E-F-C-D-B.

Thus the fifth sentence is D.

The correct answer is option 5 i.e. B

Key Points

• ‘A’ is the only sentence which can be used as the opening sentence as the use of words "Hence, But Therefore etc." in other sentences points that they must be used in between other sentences. So, A is the first statement.
• ‘E’ is in direct contrast to ‘A’ as it tries to answer what’s asked in ‘A’. So, E is the second statement.
• ‘F’ is next as it supplements the information given in ‘E’ i.e. even though we have knowledge and capacity to store we need training to be efficient. So, F is the third statement.
• ‘C’ and ‘D’ are linked and must be used together in that order. C introduces two aspects educated and uneducated and D says what they can do. So, C is the fourth statement and D is the fifth statement.
• ‘B’ is the ideal choice for closing the passage as it provides a conclusion of what’s discussed earlier. So, B is the last statement.

The correct order A-E-F-C-D-B.

The correct answer is In 1961, India was on the brink of mass famine.

Key Points

• The sentence 'In 1961, India was on the brink of mass famine.' is grammatically correct.
• The preposition 'in' is appropriate because we use it before 'years'.
• A past event is mentioned here. That is why simple past tense is used.
• The preposition 'on' which is used to express the position of something above something else is also appropriately used here.
• The definite article 'the' is also correct as something specific is mentioned here.
• Hence, the sentence is grammatically correct.
• The corrected form of the other sentences are:
• | Option | Grammatical mistake | Corrected sentence | | --- | --- | --- | | 1. | The preposition 'about' should be replaced with 'on'. | Today the dominant form of economic organization at the world level is based on market-oriented mixed economies. | | 2. | The definite article 'the' should be replaced with 'a'. | Market socialism is a form of market economy where the means of production are socially owned. | | 3. | The word 'have' should be replaced with the word 'has'. | Mexico has been called the 'birthplace' and 'burial ground' of the Green Revolution. |

 

• Therefore, option 4) is the correct answer.

Additional Information

• Brink: edge

The correct answer is The spread of Green Revolution agriculture affected both agricultural biodiversity and wild biodiversity.

Key Points

• The sentence 'The spread of Green Revolution agriculture affected both agricultural biodiversity and wild biodiversity.'
• In this given sentence a past action is mentioned. That is why, simple past tense is used here.
• The words 'agricultural' and 'wild' are appropriately to qualify the word 'biodiversity' because these are adjectives.
• Hence, this sentence is grammatically correct.
• The corrected forms of the other sentences are:
• | Option | Grammatical system | Corrected sentence | | --- | --- | --- | | 1. | The verb 'regarding' should be replaced with verb 'regarded'. | Brazil's vast inland Cerrado region was regarded as unfit for farming before the 1960s because the soil was too acidic. | | 2. | The preposition 'to' should be replaced with 'of'. | The effects of the Green Revolution on global food security are difficult to assess. | | 4. | The adverb 'acutely' should be replaced with the adjective 'acute'. | Acute health problems may occur in workers that handle pesticides. |

 

• Therefore, option 3) is the answer.

Additional Information

• Acute: severe

The correct answer is Infiltration is the process by which water enters the soil.

Key Points

The sentence 'Infiltration is the process by which water enters the soil.' is grammatically correct.

• The word 'Infiltration' is a singular noun that is why the singular verb (is) is used here.
• The definite article 'the' is appropriate before the noun 'process' and the word 'soil'.
• The word 'water' is an uncountable noun and it is treated as a singular noun that is why 's' is used at the end of the verb 'enter'.
• Hence, this sentence is grammatically correct.

The corrected form of the other sentences are:

 

Therefore, option 1) is the answer.

Additional Information

• Confluence: joining or meeting
• Envoy: a messenger or representative

The correct answer is Psychologists seek an understanding of the emergent properties of brains.

Key Points

• The sentence 'Psychologists seek an understanding of the emergent properties of brains.' is grammatically correct.
• The article 'an' should be used before the word 'understanding' as the word begins with a 'vowel' sound.
• The word 'emergent' is an adjective and it is appropriately used to qualify the noun 'properties'.
• The preposition 'of' is also correct.
• The definite article 'the' is used before the word 'emergent' because something specific is mentioned in this sentence.
• Hence, the sentence is grammatically correct.
• The corrected form of the other given sentences are:
• | Options | Grammatical mistake | Corrected sentence | | --- | --- | --- | | 1. | The preposition 'in' should be added before the word 'terms'. | Geographers attempt to understand the Earth in terms of physical and spatial relationships. | | 3. | The verb 'develop' should be replaced with the noun form 'development'. | The purpose of archaeology is to learn more about past societies and the development of the human race. | | 4. | The adjective 'previous' should be replaced with the adverb 'previously'. | Regional survey is the attempt to systematically locate previously unknown sites in a region. |

 

• Therefore, the correct answer is option 2).

Additional Information

• Spatial: relating to space
• Emergent: coming out

The correct answer is During Covid, India became the second-largest manufacturer of PPE kits in the world.

Key Points

• The sentence 'During Covid, India became the second-largest manufacturer of PPE kits in the world.' is grammatically correct.
• A past event is mentioned in the sentence, hence simple past tense is used here.
• The preposition 'during' means 'though out or in the course of'. Hence, it is appropriately used in this sentence.
• The definite article 'the' is appropriately used before the adjective 'second-largest' and also with the word 'world'.
• Hence, the sentence is grammatically correct.
• The corrected form of the other sentences are:
• | Option | Grammatical mistake | Corrected sentence | | --- | --- | --- | | 1. | The word 'transform' should be replaced with the noun 'transformation'. | Indian enterprises will continue to invest in digital transformation to take advantage of the new market opportunities. | | 2. | The verb 'expect' should be replaced with its past participle' form, i.e. 'expected'. | The restriction of inter-city and intra-city movement of non-essentials is expected to put additional pressure on existing logistics infrastructure. | | 4. | The definite article 'the' should be used before the word 'economy'. | Banking is an integral part of the economy. |

 

• Therefore, option 3) is the answer.

Additional Information

• Integral: essential or fundamental

The correct answer is 'divert, attention.'

Key Points

• The given sentence is talking about the thieves stealing items from a shop.
• ​Let us explore the words in the given options:
• 'Divert' means to draw the attention of someone from something.
• 'Attention' means notice taken of someone or something.

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Conclusion: The thieves had to draw the attention of the shopkeeper to steal the items from the shop.

Hence, the correct answer is option 4.

Complete Sentence: The thieves knew how to divert the shopkeeper’s attention so they could steal the items.

Additional Information

• The meaning of other options:
• 'Abstract' means existing only as an idea, not as a physical thing.
• 'Solace' means comfort or consolation in a time of distress or sadness.
• 'Concern' means a cause of anxiety or worry.
• 'Amuse' means to make somebody laugh or smile.
• 'Neglect' means to give too little or no attention or care to somebody or something.
• 'Harass' means to annoy or worry somebody by doing unpleasant things to him or her, especially over a long time.
• 'Ritual' means an action, ceremony, or process which is always done the same way.
• 'Aggravate' means to make something worse or more serious.

The correct answer is 'rude, trouble.'

Key Points

• The given sentence is talking about the life of teenagers.
• ​Let us explore the words in the given options:
• 'Rude' means offensively impolite or bad-mannered.
• 'Trouble' means difficulty or problems.

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Conclusion: The use of offensive or bad words often drags teenagers into trouble.

Hence, the correct answer is option 5.

Complete Sentence: Teenagers go through a phase in their life where their rude words seem to get them in trouble.

Additional Information

• The meaning of other options:
• 'Fettle' means a state of being or fitness.
• 'Adept' means very skilled or proficient at something.
• 'Salvation' means a thing or person that rescues somebody/something from danger, disaster, etc.
• 'Ripe' means ready for something or in a suitable state for something.
• 'Exposure' means the act of making something public; the thing that is made public.
• 'Evolved' means to develop or to make something develop gradually, from a simple to a more advanced form.
• 'Abide' means accept or act in accordance with a rule, decision, or recommendation.
• 'Gracious' means courteous, kind, and pleasant, especially towards someone.

The correct answer is 'argued, ​considerable.'

Key Points

• The given sentence is talking about something related to the passion of the author towards her case.
• ​Let us explore the words in the given options:
• 'Argued' means to give reasons that support your opinion about something.
• 'Considerable' means great in amount or size.

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Conclusion: The author has given reasons that support the case with great passion.

Hence, the correct answer is option 1.

Complete Sentence: She argued her case with considerable passion.

Additional Information

• The meaning of other options:
• 'Trivial' means of little value or importance.
• 'Deterred' means discouraging someone from doing something by instilling doubt or fear of the consequences.
• 'Minute' means a very short time.
• 'Enticed' means attract or tempt by offering pleasure or advantage.
• 'Meagre' means lacking in quantity or quality.
• 'Denied' means to refuse to admit or accept something.
• 'Nominal' means very small; much less than normal.
• 'Refuted' means to say that a claim is unfair and not true.

The correct answer is 'suffer, oblivion.'

Key Points

• The given sentence is talking about something related to alcoholics.
• ​Let us explore the words in the given options:
• 'Suffer' means to experience something unpleasant, for example, pain, sadness, difficulty, etc.
• 'Oblivion' means the state of being unaware or unconscious of what is happening around one.

<br>

Conclusion: Alcoholics often get unconscious after drinking alcohol.

Hence, the correct answer is option 2.

Complete Sentence: Alcoholics often suffer from periods of oblivion.

Additional Information

• The meaning of other options:
• 'Prohibit' means to say that something is not allowed by law; to forbid.
• 'Obligation' means the state of having to do something because it is a law or duty, or because you have promised.
• 'Forbid' means to not allow something.
• 'Awareness' means knowledge, consciousness, or interest.
• 'Permit' means to allow somebody to do something or to allow something to happen.
• 'Cognizance' means detailed knowledge about or understanding of something.
• 'Hinder' means to make it more difficult for somebody or something to do something.
• 'Memory' means a person’s ability to remember things.

The correct answer is Option 1)i.e. Looked into.

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Key Points

• The sense of the sentence on a whole is such that it is speaking about an event that has occurred in the past 'years ago.'
• Option 1 ‘looked’ is the correct answer because the given statement is in the past tense and the entire statement must be in the same tense.✔️
• Option 2 is incorrect because ‘look’ is in the simple present tense.❌
• Option 3 is incorrect because ‘looks’ is in the present perfect tense.❌
• Option 4 is incorrect because the given sentence is in the active voice and ‘was looked’ cannot be used in the active voice sentence.❌
• Option 5 is incorrect because the ‘looking’ is in the present continuous.❌

<br>

📌Correct sentence: The CBI officer came looked into all the evidence. The case was closed years ago. The jury was hung and could not reach a verdict.✔️

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Additional Information

• An action verb expresses an activity that a person or thing can do.
• Example: Gita eats ice cream.
• ‘eating’ is something Gita can do
• A stative verb expresses a state rather than an action. A stative verb typically relates to a state of being, a thought, or an emotion.
• Example: He believes in fairies.
• A transitive verb is one that acts on something (i.e it has a direct object)
• Example:  The postman will give Alex the letter.
• here, the direct object is the ‘letter’.

The correct answer is Option 3)i.e. How much.

Key Points

• In the given sentence, a question has been raised regarding the subject 'Daddy' instructions regarding spending. The quantity of 'spend' is the main part of this sentence.
• ‘More’ is a comparative term for quantity or extent that is used with reference to a previous quantity or against an established reference. It is used with uncountable nouns. So, option 2 is incorrect.❌
• Example: Tokyo is more populous than Beijing.
• ‘Little’ is used with uncountable nouns means small in size, degree or amount.
• ‘Little’ is considered semi-negative because it gives almost negative meaning. Hence, option 1 is incorrect.❌
• Example:  Alex had directed the little he said to her only.
• ‘A little’ is used with singular uncountable nouns mean some but less amount. It has a positive connotation. So, option 4 is incorrect.❌
• Example: I'll be fine after we rest for a little bit.
• ‘Much’ indicates the quantity or amount of a noun. We use ‘much’ only with uncountable nouns.
• In a negative sentence, “not much” means “little” or “a small amount of” an uncountable noun. The noun is in the singular form. Hence, option 3 is correct. ✔️
• Also in the given sentence, we can see that at the end 'proper amount' is mentioned, this means that we are focusing on the quantity being spent.
• Example: You may talk as much as you like.
• ‘Many’ indicates the quantity or amount of a noun. We use ‘many’ only for the countable nouns. The noun is in the plural form. Hence, option 5 is incorrect.❌
• Example: There are many animals at the zoo.

📌Correct answer: Did daddy tell you how much to spend on groceries? the markets are fluctuating widely. So we need to have a proper amount.✔️

Additional Information 

• Quantifiers are determiners** that indicate how much or how little of the noun is being discussed. They include words such as all, few, many, much, little, a little etc.**
• A determiner is a word that introduces a noun. It always comes before a noun, not after or any other adjectives used to describe the noun.
• There are four different types of determiners: articles, demonstrative, quantifiers and possessives.

The correct answer is Option 3)i.e. used to play.

Key Points

• Upon reading the given sentence we see that:
• The sentence talks about the matter in which the committee is involved.
• ‘used to’ is present before the blank which indicated that the action was done in past.
• ‘used to’ is always followed by an infinitive if it talks about a past event.
• Here,‘ to play ’ is the infinitive of ‘play’.
• The correct phrase is 'to play.'✔️

📌Correct sentence: He used to play football professionally but he had to quit because of an injury.✔️

Additional Information 

• Let us look at the use of other words:
• Playing is the continuous tense of the verb ‘play’. It is also the gerund and participle of the verb.
• Played is the past participle of the verb ‘play’.
• Had played is used for past perfect tense.
• Has played is used for present perfect tense.

General solution:

 

College A:

Number students studying in college  = 2500 ×  (18/100) = 450

Number of male students studying = 1200 ×  (25/100) = 300

Number of female students studying = (450 - 300) = 150

 

College B:

Number students studying in college  = 2500 ×  (24/100) = 600

Number of male students studying = 1200 ×  (15/100) = 180

Number of female students studying = (600 - 180) = 420

 

College C:

Number students studying in college  = 2500 ×  (15/100) = 375

Number of male students studying = 1200 ×  (20/100) = 240

Number of female students studying = (375 - 240) = 135

 

College D:

Number students studying in college  = 2500 ×  (23/100) = 575

Number of male students studying = 1200 ×  (18/100) = 216

Number of female students studying = (575 - 216) = 359

 

College E:

Number students studying in college  = 2500 ×  (20/100) = 500

Number of male students studying = 1200 ×  (22/100) = 264

Number of female students studying = (500 - 264) = 236

 

 

Solution:

Number of male students studying in A = 300

Number of male students studying in B = 180

Number of female students studying in A = 150

Number of female students studying B = 420

Required ratio = (300 + 180): (150+ 420) = (480 : 570) = 48: 57

General solution:

 

College A:

Number students studying in college  = 2500 ×  (18/100) = 450

Number of male students studying = 1200 ×  (25/100) = 300

Number of female students studying = (450 - 300) = 150

 

College B:

Number students studying in college  = 2500 ×  (24/100) = 600

Number of male students studying = 1200 ×  (15/100) = 180

Number of female students studying = (600 - 180) = 420

 

College C:

Number students studying in college  = 2500 ×  (15/100) = 375

Number of male students studying = 1200 ×  (20/100) = 240

Number of female students studying = (375 - 240) = 135

 

College D:

Number students studying in college  = 2500 ×  (23/100) = 575

Number of male students studying = 1200 ×  (18/100) = 216

Number of female students studying = (575 - 216) = 359

 

College E:

Number students studying in college  = 2500 ×  (20/100) = 500

Number of male students studying = 1200 ×  (22/100) = 264

Number of female students studying = (500 - 264) = 236

 

 

Solution:

Number of males more than 30 years from college A = 300 × 1/4 = 75

Number of males less than 30 years from college A = (300 - 75) = 225

Number of females less than 30 years from college A = 3/5 ×  150 = 90

Number of females more than 30 years = (150 - 90) = 60

Required difference = 225 - 60 = 165

General solution:

 

College A:

Number students studying in college  = 2500 ×  (18/100) = 450

Number of male students studying = 1200 ×  (25/100) = 300

Number of female students studying = (450 - 300) = 150

 

College B:

Number students studying in college  = 2500 ×  (24/100) = 600

Number of male students studying = 1200 ×  (15/100) = 180

Number of female students studying = (600 - 180) = 420

 

College C:

Number students studying in college  = 2500 ×  (15/100) = 375

Number of male students studying = 1200 ×  (20/100) = 240

Number of female students studying = (375 - 240) = 135

 

College D:

Number students studying in college  = 2500 ×  (23/100) = 575

Number of male students studying = 1200 ×  (18/100) = 216

Number of female students studying = (575 - 216) = 359

 

College E:

Number students studying in college  = 2500 ×  (20/100) = 500

Number of male students studying = 1200 ×  (22/100) = 264

Number of female students studying = (500 - 264) = 236

 

 

Solution:

Total females in college A = 150

Number of females from college A from cities = 150 ×  40/100 = 60

Number of females from college A from village = (150 - 60) = 90

Number of females from college D = 359

Required total = (359 + 90) = 449

General solution:

 

College A:

Number students studying in college  = 2500 ×  (18/100) = 450

Number of male students studying = 1200 ×  (25/100) = 300

Number of female students studying = (450 - 300) = 150

 

College B:

Number students studying in college  = 2500 ×  (24/100) = 600

Number of male students studying = 1200 ×  (15/100) = 180

Number of female students studying = (600 - 180) = 420

 

College C:

Number students studying in college  = 2500 ×  (15/100) = 375

Number of male students studying = 1200 ×  (20/100) = 240

Number of female students studying = (375 - 240) = 135

 

College D:

Number students studying in college  = 2500 ×  (23/100) = 575

Number of male students studying = 1200 ×  (18/100) = 216

Number of female students studying = (575 - 216) = 359

 

College E:

Number students studying in college  = 2500 ×  (20/100) = 500

Number of male students studying = 1200 ×  (22/100) = 264

Number of female students studying = (500 - 264) = 236

 

 

Solution:

 

Number of female students in college C participating in sports competition = 2/5 ×  135 = 54

Number of female students in college E participating in sports competition =236 ×  1/2 = 118

Total number of students participating in sports from college C = 375 ×  2/3 = 250

Total number of students participating in sports from college E = 500 ×  3/5 = 300

Number of male participating in sports from college C = 250 - 54 = 196

Number of male participating in sports from college E = 300 - 118 = 182

Total number of males participating in sports competition from C and E = (196 + 182) = 378

General solution:

 

College A:

Number students studying in college  = 2500 ×  (18/100) = 450

Number of male students studying = 1200 ×  (25/100) = 300

Number of female students studying = (450 - 300) = 150

 

College B:

Number students studying in college  = 2500 ×  (24/100) = 600

Number of male students studying = 1200 ×  (15/100) = 180

Number of female students studying = (600 - 180) = 420

 

College C:

Number students studying in college  = 2500 ×  (15/100) = 375

Number of male students studying = 1200 ×  (20/100) = 240

Number of female students studying = (375 - 240) = 135

 

College D:

Number students studying in college  = 2500 ×  (23/100) = 575

Number of male students studying = 1200 ×  (18/100) = 216

Number of female students studying = (575 - 216) = 359

 

College E:

Number students studying in college  = 2500 ×  (20/100) = 500

Number of male students studying = 1200 ×  (22/100) = 264

Number of female students studying = (500 - 264) = 236

 

 

Solution:

Total number of female in college B = 420

Number of female doing Post graduate evening shift in college B = (216 + 264)/2 = 240

Number of female doing Post graduate Morning shift in college B = (420 - 240) = 180

Number of female students in college A = 150

Required difference = (180 - 150) = 30

Shortcut Trick

Total Votes = 84000

Valid Votes = 75% of 84000 = 63000

Winner got 70% of Valid Votes → Other candidate got 30% of Valid Votes.

Other Candidate Votes = 30% of 63000 = 18900.

∴ The correct answer is 18900.

Alternate Method

Given:

Total number of votes = 84000

Invalid votes = 25%

Winner's share = 70% of valid votes

Calculations:

⇒ Valid votes = Total votes − 25% of Total votes

⇒ Valid votes = 84000 × (75/100) = 63000

⇒ Since the winner got 70% of valid votes, the other candidate got (100 − 70) = 30% of valid votes.

⇒ Other candidate's votes = 30% of 63000

⇒ Other candidate's votes = (30/100) × 63000 = 18900

∴ The correct answer is 18900.

Additional Information

Election Based Percentages

In election problems, always distinguish between total votes, votes cast, and valid votes. The winning margin is usually calculated on valid votes.

Successive Percentage

The calculation can be combined as: Final Value = Total × (Valid % / 100) × (Candidate % / 100).

Shortcut Trick

Total Work (LCM of 21 and 15) = 105 units.

Efficiency of Sunita = 105 ÷ 21 = 5 units/day.

Efficiency of Sarita = 105 ÷ 15 = 7 units/day.

Work done by Sarita in 10 days = 7 × 10 = 70 units.

Remaining work = 105 − 70 = 35 units.

Time taken by Sunita = 35 ÷ 5 = 7 days.

∴ The correct answer is 7 days.

Alternate Method

Given:

Time taken by Sunita = 21 days

Time taken by Sarita = 15 days

Calculations:

⇒ Total work = LCM(21, 15) = 105 units

⇒ 1 day work of Sarita = 105 ÷ 15 = 7 units

⇒ Work completed by Sarita in 10 days = 7 × 10 = 70 units

⇒ Remaining work = 105 − 70 = 35 units

⇒ 1 day work of Sunita = 105 ÷ 21 = 5 units

⇒ Time taken by Sunita to complete remaining work = 35 ÷ 5 = 7 days

∴ The correct answer is 7 days.

Additional Information

Work and Efficiency Relation

Total Work = Efficiency × Time. Efficiency is inversely proportional to the time taken to complete the work.

Remaining Work Formula

Time for remaining work = (Total Work − Work already done) ÷ Efficiency of the person completing it.

LCM Method

Assuming Total Work as the Least Common Multiple (LCM) of the given number of days simplifies calculations by avoiding fractions.

Given series:

244, 100, 269, 73, 298, (?)

The logic followed here is:

⇒ 244 - (12)² = 100

⇒ 100 + (13)2 = 269

⇒ 269 - (14)2 = 73

⇒ 73 + (15)2 = 298

⇒ 298 - (16)2 = 42

Hence, 42 will come in the place of (?).

Given Series:

121, 130, 119, 132, (?), 134

The logic followed here is as follows:

⇒ 121 + 9 = 130

⇒ 130 - 11 = 119

⇒ 119 + 13 = 132

⇒ 132 - 15 = 117

⇒ 117 + 17 = 134

Hence, 117 will come in the place of (?).

Given Series:

2, 3, 5, 9, 17, (?), 65

The logic followed here is as follows:

⇒ 2 + 1 = 3

⇒ 3 + 2 = 5

⇒ 5 + 4 = 9

⇒ 9 + 8 = 17

⇒ 17 + 16 = 33

⇒ 33 + 32 = 65

Hence, 33 will come in the place of (?).

The series follows the following pattern

 ⇒ 17 + 20 = 37

 ⇒ 37 + 40 = 77

 ⇒ 77 + 60 = 137

 ⇒ 137 + 80 = 217

 ⇒ 217 + 100 = 317 

Hence, the correct answer is 317.

Solution :

The series follows the following pattern :

⇒2000 × 0.1 = 200

⇒200 × 0.2 = 40

⇒40 × 0.3 = 12

⇒12 × 0.4 = 4.8

⇒4.8 × 0.5 = 2.4

⇒ The next term in the series will be 2.4.

Hence, 2.4 is the correct answer.

Shortcut Trick

Simple Interest rate: 3/4 of sum in 3 years → 1/4 of sum per year → 25% per annum.

For Compound Interest at 25% for 2 years, the Multiplying Factor is (1.25)² = 1.5625.

Amount = 1500 × 1.5625 = 2343.75.

∴ The correct answer is Rs. 2343.75.

Alternate Method

Given: Time (T₁) = 3 years, SI = 3/4 × P₁, P₂ = Rs. 1500, T₂ = 2 years.

Formula Used: SI = (P × R × T)/100; Amount (CI) = P(1 + R/100)ⁿ

⇒ 3/4 × P = (P × R × 3)/100

⇒ 1/4 = R/100

⇒ Rate (R) = 25%

⇒ Amount = 1500 × (1 + 25/100)²

⇒ Amount = 1500 × (5/4) × (5/4)

⇒ Amount = 1500 × 25/16

⇒ Amount = 37500 / 16 = 2343.75

∴ The correct answer is Rs. 2343.75.

Additional Information

Compound Interest Formula

The total amount A is calculated as A = P(1 + r/n)^nt, where n is the number of times interest is compounded per year.

Effective Rate for 2 Years

For a rate R, the effective CI rate for 2 years is R + R + (R×R)/100. For 25%, it is 25 + 25 + 6.25 = 56.25%.

SI vs CI Difference

Difference between CI and SI for 2 years is P(R/100)².

Shortcut Trick

Let the initial mixture P be 100 units.

Initial Lime Juice = 45 units, Water = 55 units.

Ratio: (45 + x) / (55 + 2x) = 15 / 23

Cross-multiplying: 23(45 + x) = 15(55 + 2x) → 1035 + 23x = 825 + 30x → 7x = 210 → x = 30.

Ratio of P to x = 100 : 30 = 10 : 3.

∴ The correct answer is 10:3.

Alternate Method

Given:

Initial Lime Juice in P = 45%

Initial Water in P = 100% − 45% = 55%

Added Lime Juice = x, Added Water = 2x

Final Ratio = 15 : 23

Calculations:

Let the total initial quantity of Mixture P be Q.

⇒ Lime Juice in P = 0.45Q

⇒ Water in P = 0.55Q

⇒ (0.45Q + x) / (0.55Q + 2x) = 15 / 23

⇒ 23 × (0.45Q + x) = 15 × (0.55Q + 2x)

⇒ 10.35Q + 23x = 8.25Q + 30x

⇒ 10.35Q − 8.25Q = 30x − 23x

⇒ 2.1Q = 7x

⇒ Q / x = 7 / 2.1 = 70 / 21 = 10 / 3

∴ The correct answer is 10:3.

Additional Information

Mixture and Alligation

When two ingredients are mixed, the ratio of quantities is inversely proportional to the difference between their individual concentrations and the mean concentration.

Ratio and Proportion

If a/b = c/d, then by cross-multiplication ad = bc. This property is vital for solving linear equations involving ratios.

Percentage to Ratio Conversion

A concentration of 45% can be written as the fraction 45/100 or the ratio 9:11 (9 parts juice to 11 parts water).

General Solution:

 

School A:

Total number of boys and girls in school A = 275 ×  2 = 550

Difference between Number of boys and girls is 50

B + G = 550

B - G = 50

2B = 600

B = 300

Number of boys in school = 300

Number of girls in school = 550 - 300 = 250

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 250 - 150 = 100

 

School B:

Total number of boys and girls in school B = 375 ×  2 = 750

Difference between Number of boys and girls is 50

G + B = 750

G - B = 50

2G = 800

G = 400

Number of girls in school = 400

Number of boys in school = 750 - 400 = 350

Number of boys and girls having chocolate = 200

Number of girls having chocolate = 300 - 200 = 100

 

School C:

Total number of boys and girls in school C = 375 ×  2 = 750

Difference between Number of boys and girls is 150

B + G = 750

B - G = 150

2B = 900

B = 450

Number of boys in school = 450

Number of girls in school = 750 - 450 = 300

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 400 - 150 = 250

 

School D:

Total number of boys and girls in school D = 475 ×  2 = 950

Difference between Number of boys and girls is 50

B + G = 950

B - G = 50

2B = 1000

B = 500

Number of boys in school = 500

Number of girls in school = 950 - 500 = 450

Number of boys and girls having chocolate = 350

Number of girls having chocolate = 350 - 200 = 150

 

School E:

Total number of boys and girls in school E = 225 ×  2 = 450

Difference between Number of boys and girls is 50

B + G = 450

B - G = 50

2B = 500

B = 250

Number of boys in school = 250

Number of girls in school = 450 - 250 = 200

Number of boys and girls having chocolate = 100

Number of girls having chocolate = 300 - 100 = 200

 

 

Solution:

Number of chocolate having students in school E = (200 + 100) = 300

Number of girls in school E = 200

Required percentage = (300 - 200)/200 ×  100 = 50%

General Solution:

 

School A:

Total number of boys and girls in school A = 275 ×  2 = 550

Difference between Number of boys and girls is 50

B + G = 550

B - G = 50

2B = 600

B = 300

Number of boys in school = 300

Number of girls in school = 550 - 300 = 250

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 250 - 150 = 100

 

School B:

Total number of boys and girls in school B = 375 ×  2 = 750

Difference between Number of boys and girls is 50

G + B = 750

G - B = 50

2G = 800

G = 400

Number of girls in school = 400

Number of boys in school = 750 - 400 = 350

Number of boys and girls having chocolate = 200

Number of girls having chocolate = 300 - 200 = 100

 

School C:

Total number of boys and girls in school C = 375 ×  2 = 750

Difference between Number of boys and girls is 150

B + G = 750

B - G = 150

2B = 900

B = 450

Number of boys in school = 450

Number of girls in school = 750 - 450 = 300

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 400 - 150 = 250

 

School D:

Total number of boys and girls in school D = 475 ×  2 = 950

Difference between Number of boys and girls is 50

B + G = 950

B - G = 50

2B = 1000

B = 500

Number of boys in school = 500

Number of girls in school = 950 - 500 = 450

Number of boys and girls having chocolate = 350

Number of girls having chocolate = 350 - 200 = 150

 

School E:

Total number of boys and girls in school E = 225 ×  2 = 450

Difference between Number of boys and girls is 50

B + G = 450

B - G = 50

2B = 500

B = 250

Number of boys in school = 250

Number of girls in school = 450 - 250 = 200

Number of boys and girls having chocolate = 100

Number of girls having chocolate = 300 - 100 = 200

 

 

Solution:

Number of boys in school D = 500 ×  140/100 = 700

Number of girls in school D = 450 ×  120/100 = 540

Number of chocolate required to boys = 700 - 200 = 500

Number of chocolate required to girls = 540 - 150 = 390

Required difference = (500 - 390) = 110

General Solution:

 

School A:

Total number of boys and girls in school A = 275 ×  2 = 550

Difference between Number of boys and girls is 50

B + G = 550

B - G = 50

2B = 600

B = 300

Number of boys in school = 300

Number of girls in school = 550 - 300 = 250

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 250 - 150 = 100

 

School B:

Total number of boys and girls in school B = 375 ×  2 = 750

Difference between Number of boys and girls is 50

G + B = 750

G - B = 50

2G = 800

G = 400

Number of girls in school = 400

Number of boys in school = 750 - 400 = 350

Number of boys and girls having chocolate = 200

Number of girls having chocolate = 300 - 200 = 100

 

School C:

Total number of boys and girls in school C = 375 ×  2 = 750

Difference between Number of boys and girls is 150

B + G = 750

B - G = 150

2B = 900

B = 450

Number of boys in school = 450

Number of girls in school = 750 - 450 = 300

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 400 - 150 = 250

 

School D:

Total number of boys and girls in school D = 475 ×  2 = 950

Difference between Number of boys and girls is 50

B + G = 950

B - G = 50

2B = 1000

B = 500

Number of boys in school = 500

Number of girls in school = 950 - 500 = 450

Number of boys and girls having chocolate = 350

Number of girls having chocolate = 350 - 200 = 150

 

School E:

Total number of boys and girls in school E = 225 ×  2 = 450

Difference between Number of boys and girls is 50

B + G = 450

B - G = 50

2B = 500

B = 250

Number of boys in school = 250

Number of girls in school = 450 - 250 = 200

Number of boys and girls having chocolate = 100

Number of girls having chocolate = 300 - 100 = 200

 

 

Solution:

Ratio of number of boys to girls present in school C = 450: 300 = 3:2

Number of chocolate distributed to boys = 200/5 ×  3 = 120

Number of chocolate distributed to girls = (200 - 120) = 80

Number of boys having chocolate at present is (150 + 120) = 270

General Solution:

 

School A:

Total number of boys and girls in school A = 275 ×  2 = 550

Difference between Number of boys and girls is 50

B + G = 550

B - G = 50

2B = 600

B = 300

Number of boys in school = 300

Number of girls in school = 550 - 300 = 250

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 250 - 150 = 100

 

School B:

Total number of boys and girls in school B = 375 ×  2 = 750

Difference between Number of boys and girls is 50

G + B = 750

G - B = 50

2G = 800

G = 400

Number of girls in school = 400

Number of boys in school = 750 - 400 = 350

Number of boys and girls having chocolate = 200

Number of girls having chocolate = 300 - 200 = 100

 

School C:

Total number of boys and girls in school C = 375 ×  2 = 750

Difference between Number of boys and girls is 150

B + G = 750

B - G = 150

2B = 900

B = 450

Number of boys in school = 450

Number of girls in school = 750 - 450 = 300

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 400 - 150 = 250

 

School D:

Total number of boys and girls in school D = 475 ×  2 = 950

Difference between Number of boys and girls is 50

B + G = 950

B - G = 50

2B = 1000

B = 500

Number of boys in school = 500

Number of girls in school = 950 - 500 = 450

Number of boys and girls having chocolate = 350

Number of girls having chocolate = 350 - 200 = 150

 

School E:

Total number of boys and girls in school E = 225 ×  2 = 450

Difference between Number of boys and girls is 50

B + G = 450

B - G = 50

2B = 500

B = 250

Number of boys in school = 250

Number of girls in school = 450 - 250 = 200

Number of boys and girls having chocolate = 100

Number of girls having chocolate = 300 - 100 = 200

 

 

Solution:

Number of boys having chocolate from school B = 200

Number of boys having chocolate from school C = 150

Number of girls having chocolate from school D = 150

Number of girls having chocolate from school E = 200

Required ratio = 350: 350 = 1: 1

General Solution:

 

School A:

Total number of boys and girls in school A = 275 ×  2 = 550

Difference between Number of boys and girls is 50

B + G = 550

B - G = 50

2B = 600

B = 300

Number of boys in school = 300

Number of girls in school = 550 - 300 = 250

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 250 - 150 = 100

 

School B:

Total number of boys and girls in school B = 375 ×  2 = 750

Difference between Number of boys and girls is 50

G + B = 750

G - B = 50

2G = 800

G = 400

Number of girls in school = 400

Number of boys in school = 750 - 400 = 350

Number of boys and girls having chocolate = 200

Number of girls having chocolate = 300 - 200 = 100

 

School C:

Total number of boys and girls in school C = 375 ×  2 = 750

Difference between Number of boys and girls is 150

B + G = 750

B - G = 150

2B = 900

B = 450

Number of boys in school = 450

Number of girls in school = 750 - 450 = 300

Number of boys and girls having chocolate = 150

Number of girls having chocolate = 400 - 150 = 250

 

School D:

Total number of boys and girls in school D = 475 ×  2 = 950

Difference between Number of boys and girls is 50

B + G = 950

B - G = 50

2B = 1000

B = 500

Number of boys in school = 500

Number of girls in school = 950 - 500 = 450

Number of boys and girls having chocolate = 350

Number of girls having chocolate = 350 - 200 = 150

 

School E:

Total number of boys and girls in school E = 225 ×  2 = 450

Difference between Number of boys and girls is 50

B + G = 450

B - G = 50

2B = 500

B = 250

Number of boys in school = 250

Number of girls in school = 450 - 250 = 200

Number of boys and girls having chocolate = 100

Number of girls having chocolate = 300 - 100 = 200

 

 

Solution:

Number of boys having chocolate in school A = 150 ×  120/100 = 180

Number of girls having chocolate in school A= 100 ×  125/100 = 125

Number of boys not having chocolate in school A = (300 - 180) = 120

Number of girls not having chocolate in school A = (250 - 125) = 125

Required difference = (125 - 120) = 5

Shortcut Trick

Ratio of CP of 1 apple to 1 orange = 5 : 2. Let CP of 1 apple = 5 and 1 orange = 2.

Total CP of 8 apples and 10 oranges = (8 × 5) + (10 × 2) = 40 + 20 = 60.

Profit on 8 apples: CP of 8 = SP of 5 ⇒ SP of 8 = (8 ÷ 5) × CP of 8 = 1.6 × 40 = 64.

Profit on 10 oranges: CP of 13 = SP of 10 ⇒ SP of 10 = CP of 13 = 13 × 2 = 26.

Total SP = 64 + 26 = 90. Profit % = [(90 − 60) ÷ 60] × 100 = 50%.

∴ The correct answer is 50%.

Alternate Method

Given → 8 CP_a = 5 SP_a, 13 CP_o = 10 SP_o, CP_a : CP_o = 5 : 2. Formulas: Profit = SP − CP | Profit % = (Profit ÷ CP) × 100.

⇒ Let CP of 1 apple = 5x and CP of 1 orange = 2x. ⇒ Total CP of 8 apples and 10 oranges = 8(5x) + 10(2x) = 40x + 20x = 60x. ⇒ For apples: 5 SP_a = 8 CP_a ⇒ SP of 5 apples = 8(5x) = 40x ⇒ SP of 1 apple = 8x. ⇒ SP of 8 apples = 8 × 8x = 64x. ⇒ For oranges: 10 SP_o = 13 CP_o ⇒ SP of 10 oranges = 13(2x) = 26x. ⇒ Total SP = 64x + 26x = 90x. ⇒ Net Profit % = [(90x − 60x) ÷ 60x] × 100 = (30 ÷ 60) × 100 = 50%.

∴ The correct answer is 50%.

Additional Information

Profit and Loss on Multiple Articles

When handling different items, find the total cost price and total selling price separately before calculating the overall profit percentage.

Ratio of CP and SP

If n CP = m SP, then the ratio of CP/SP = m/n. This allows for quick calculation of individual item profits.

Shortcut Trick

Assume third number = 1 unit.

Second number = 3 units, First number = 6 units, Fourth number = 4 units.

Total units = 6 + 3 + 1 + 4 = 14 units.

Sum of numbers = 14 × 4 = 56.

14 units = 56 ⇒ 1 unit = 4.

Fourth number = 4 units = 4 × 4 = 16.

∴ The correct answer is 16.

Alternate Method

Given: Average of 4 numbers = 14. Relations between numbers are provided.

Formula: Sum = Average × Count of numbers.

⇒ Let the third number be x.

⇒ Second number = 3x.

⇒ First number = 2 × 3x = 6x.

⇒ Third number = (1/4) × Fourth number ⇒ Fourth number = 4x.

⇒ Average = (6x + 3x + x + 4x) ÷ 4 = 14.

⇒ 14x ÷ 4 = 14.

⇒ 14x = 56.

⇒ x = 4.

⇒ Fourth number = 4x = 4 × 4 = 16.

∴ The correct answer is 16.

Additional Information

Average Concept

Average is the sum of observations divided by the total number of observations. Formula: Sum = Average × Number of terms.

Ratio and Proportion

When multiple variables are related linearly, always assume the most central or smallest variable as a single unit (x) to simplify calculations.

I. x² + 5x – 104 = 0

⇒ x² + 13x – 8x – 104 = 0

⇒ x(x + 13) – 8(x + 13) = 0

⇒ (x + 13) (x – 8) = 0

⇒ x = –13, 8

 

II. y² + 30y + 224 = 0

⇒ y² + 16y + 14y + 224 = 0

⇒ y(y + 16) + 14(y + 16) = 0

⇒ (y + 16) (y + 14) = 0

⇒ y = –16, –14

 

 

∴ x > y

I. 2x² + 5x – 3 = 0

⇒ 2x² + 6x – x – 3 = 0

⇒ 2x (x + 3) – 1 (x + 3) = 0

⇒ (2x – 1) (x + 3) = 0,

⇒ x = 1/2, – 3

 

II. 2y² – 5y + 2 = 0

⇒ 2y² – 4y – y + 2 = 0

⇒ 2y (y – 2) – 1 (y – 2) = 0

⇒ (2y – 1) (y – 2) = 0

⇒ y = 1/2, 2

 

Hence, x ≤ y

I. x² – 38x + 360 = 0

⇒ x²– 20x – 18x + 360 = 0

⇒ (x – 18) (x – 20) = 0

⇒ x = 18, 20

II. y²+ 10y + 24 = 0

⇒ y² + 6y + 4y + 2 = 0

⇒ (y + 4) (y + 6) = 0

⇒ y = –4, –6

 

Hence, x > y.

I. x² – 20x + 99 = 0

⇒ x² – 11x – 9x + 99 = 0

⇒ x (x – 11) – 9 (x – 11) = 0

⇒ (x – 11) (x – 9) = 0

⇒ x = 11, 9

 

II. y² – 9y + 20 = 0

⇒ y² – 5y – 4y + 20 = 0

⇒ y (y – 5) – 4 (y – 5) = 0

⇒ (y – 5) (y – 4) = 0

⇒ y = 5, 4

 

 

Hence x > y

I. 6x² – 17x + 5 = 0

⇒ 6x² – 15x – 2x + 5 = 0

⇒ 3x (2x – 5) – 1 (2x – 5) = 0

⇒ (2x – 5) (3x – 1) = 0

⇒ x = 5/2, 1/3

 

II. 10y² + 3y – 1 = 0

⇒ 10y² + 5y – 2y – 1 = 0

⇒ 5y (2y + 1) – 1 (2y + 1) = 0

⇒ (2y + 1) (5y – 1) = 0

⇒ y = -1/2, 1/5

Comparison between x and y (via Tabulation):

 

∴  x > y

General Solution:

The number of Cotton Sarees sold in Shop A = 5x

The number of Silk Sarees sold in Shop A = 530 – 5x

The number of Cotton Sarees sold in Shop C = 6x

The number of Cotton Sarees sold in Shop B = y

The number of Silk Sarees sold in Shop C = y – 55

The number of Silk Sarees sold in Shop B = 6x + 20

The number of Cotton Sarees sold in Shop A is 30 more than the number of Silk Sarees sold

in Shop C

5x = 30 + y – 55

y = 5x + 25 ----------- (1)

The total number of Cotton Sarees sold in all three shops is 825

5x + y + 6x = 825

5x + 5x + 25 + 6x = 825

16x = 800

x = 50

Substitute x = 50 in equation (1)

y = 5 ×  50 + 25

y = 275

Solution:

Total number of Silk Sarees sold = (280 + 320 + 220) = 820

Total number of Cotton Sarees sold = (250 + 275 + 300) = 825

Required difference = (825 – 820) = 5

General Solution:

The number of Cotton Sarees sold in Shop A = 5x

The number of Silk Sarees sold in Shop A = 530 – 5x

The number of Cotton Sarees sold in Shop C = 6x

The number of Cotton Sarees sold in Shop B = y

The number of Silk Sarees sold in Shop C = y – 55

The number of Silk Sarees sold in Shop B = 6x + 20

The number of Cotton Sarees sold in Shop A is 30 more than the number of Silk Sarees sold

in Shop C

5x = 30 + y – 55

y = 5x + 25 ----------- (1)

The total number of Cotton Sarees sold in all three shops is 825

5x + y + 6x = 825

5x + 5x + 25 + 6x = 825

16x = 800

x = 50

Substitute x = 50 in equation (1)

y = 5 ×  50 + 25

y = 275

Solution:

Number of Cotton Sarees sold in Shop A = 250 ×  (130/100) = 325

Number of Silk Sarees sold in Shop A = 280 ×  (125/100) = 350

Required sum = 325 + 350 = 675

General Solution:

The number of Cotton Sarees sold in Shop A = 5x

The number of Silk Sarees sold in Shop A = 530 – 5x

The number of Cotton Sarees sold in Shop C = 6x

The number of Cotton Sarees sold in Shop B = y

The number of Silk Sarees sold in Shop C = y – 55

The number of Silk Sarees sold in Shop B = 6x + 20

The number of Cotton Sarees sold in Shop A is 30 more than the number of Silk Sarees sold

in Shop C

5x = 30 + y – 55

y = 5x + 25 ----------- (1)

The total number of Cotton Sarees sold in all three shops is 825

5x + y + 6x = 825

5x + 5x + 25 + 6x = 825

16x = 800

x = 50

Substitute x = 50 in equation (1)

y = 5 ×  50 + 25

y = 275

Solution:

The sum of the number of Silk Sarees sold in Shop B and C = 320 + 220 = 540

The number of Cotton Sarees sold in Shop C = 300

Required percentage = [(540 – 300)/300] ×  100

= [240/300] ×  100

= 80%

Shortcut Trick

Volume of Cylindrical Bucket = Volume of Conical Heap.

π × r_c² × h_c = (1/3) × π × r_h² × h_h

18² × 32 = (1/3) × r_h² × 24

r_h² = (324 × 32 × 3) / 24 = 1296

Area covered = πr_h² = (22/7) × 1296 ≈ 4073.14 cm².

∴ The correct answer is 4073.14 cm².

Alternate Method

Given: Radius of Cylindrical Bucket (r) = 18 cm, Height (h) = 32 cm. Height of Conical Heap (H) = 24 cm.

Formula Used: Volume of Cylinder = πr²h; Volume of Cone = (1/3)πR²H; Area of base = πR².

⇒ Volume of sand = π × (18)² × 32

⇒ Volume of conical heap = (1/3) × π × R² × 24

⇒ (1/3) × π × R² × 24 = π × 324 × 32

⇒ 8 × R² = 324 × 32

⇒ R² = 324 × 4 = 1296 cm²

⇒ Area covered on ground = Area of circular base of cone = πR²

⇒ Area = (22/7) × 1296 = 28512 / 7 ≈ 4073.1428...

∴ The correct answer is 4073.14 cm².

Additional Information

Volume Invariance

When a 3D object is reshaped or its contents are poured out to form a new shape, the Total Volume remains constant.

Cone Geometry

The area covered by a conical heap on a flat surface is the area of its Circular Base, calculated as A = πr².

Slant Height of Cone

Slant height l = √(R² + H²), which is used for calculating the Curved Surface Area (πRl).

Shortcut Trick

Ratio of Lengths = (Ratio of Speed) × (Ratio of Time)

L_A : L_B = (4 × 5) : (7 × 3) = 20 : 21

Total units = 20 + 21 = 41 units → 410 m

Difference = 21 − 20 = 1 unit → (410 ÷ 41) × 1 = 10 m

∴ The correct answer is 10 m.

Alternate Method

Given: Sum of lengths (L_A + L_B) = 410 m; Ratio of speeds (S_A : S_B) = 4 : 7; Ratio of time (T_A : T_B) = 5 : 3.

Formula: Length of train = Speed × Time (to cross a pole)

⇒ Let S_A = 4x, S_B = 7x and T_A = 5y, T_B = 3y

⇒ L_A = 4x × 5y = 20xy

⇒ L_B = 7x × 3y = 21xy

⇒ L_A + L_B = 20xy + 21xy = 41xy

⇒ 41xy = 410 ⇒ xy = 10

⇒ Difference = L_B − L_A = 21xy − 20xy = xy

⇒ Difference = 10 m

∴ The correct answer is 10 m.

Additional Information

Relative Speed

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

Crossing Objects

To cross a pole/man, distance = length of train. To cross a platform/bridge, distance = length of train + length of platform.

Unit Conversion

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

Shortcut Trick

Ratio of Speed of Boat (u) to Speed of Stream (v) = 5 : 2

Downstream speed (D) = 5 + 2 = 7 units; Upstream speed (U) = 5 − 2 = 3 units

Time difference = 42/3x − 42/7x = 4 ⇒ 14/x − 6/x = 4 ⇒ 8/x = 4 ⇒ x = 2

Speed of boat in still water = 5 × 2 = 10 km/hr

∴ The correct answer is 10 km/hr.

Alternate Method

Given: Ratio u : v = 5 : 2. Distance (D) = 42 km. Time difference = 4 hours.

Formula Used: Time = Distance ÷ Speed; Downstream Speed = u + v; Upstream Speed = u − v.

⇒ Let Speed of boat = 5x and Speed of stream = 2x

⇒ Upstream Speed = 3x; Downstream Speed = 7x

⇒ Time Upstream − Time Downstream = 4 hours

⇒ 42/3x − 42/7x = 4

⇒ 14/x − 6/x = 4

⇒ 8/x = 4 ⇒ x = 2

⇒ Speed of boat = 5 × 2 = 10 km/hr

∴ The correct answer is 10 km/hr.

Additional Information

Speed in Still Water

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

Speed of Current

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

Relative Speed in Streams

When moving downstream, speeds add up; when moving upstream, the stream speed is subtracted from the boat speed.

Shortcut Trick

Initial Ratio R : P : S = 7 : 6 : 9 (Total parts = 22)

Final Ratio R : P : S = 5 : 3 : 3 (Multiply by 2 to equate Puneet's balls) → 10 : 6 : 6 (Total parts = 22)

Change in Sweety's balls = 9 − 6 = 3 units | Change in Rinku's balls = 10 − 7 = 3 units

3 units = 15 balls ⇒ 1 unit = 5 balls

Initial Rinku's balls = 7 units = 7 × 5 = 35 balls.

∴ The correct answer is 35 balls.

Alternate Method

Given: Initial ratio of balls with Rinku, Puneet and Sweety = 7 : 6 : 9.

Formula: Ratio = Value ÷ Common Factor (x)

⇒ Let balls be 7x, 6x, and 9x.

⇒ According to question: (7x + 15) / 6x / (9x − 15) = 5 / 3 / 3

⇒ Comparing Puneet and Sweety: 6x / (9x − 15) = 3 / 3

⇒ 6x = 9x − 15

⇒ 3x = 15 ⇒ x = 5

⇒ Initial balls with Rinku = 7x = 7 × 5 = 35.

∴ The correct answer is 35 balls.

Additional Information

Ratio Constancy Principle

When items are transferred between two people in a group, the total sum of items in the group remains constant. Always equate the total parts of ratios to simplify calculations.

Compound Ratio

If two ratios are a : b and c : d, then the compound ratio is (a × c) : (b × d).

Shortcut Trick

Let A's present age be 1 unit.

Mother's present age = 6 units.

Sum of Mother and Father after 5 years = 80 years → Present sum = 80 − 10 = 70 years.

Since Father is 10 years older, 2 × Mother + 10 = 70 ⇒ Mother = 30 years.

6 units = 30 years ⇒ 1 unit = 5 years.

∴ The correct answer is 5 years.

Alternate Method

Given:

Let A's present age = x

Mother's age (M) = 6x

Father's age (F) = M + 10 = 6x + 10

Calculations:

⇒ Sum of ages of Mother and Father after 5 years = (M + 5) + (F + 5) = 80

⇒ M + F + 10 = 80

⇒ M + F = 70

⇒ 6x + (6x + 10) = 70

⇒ 12x + 10 = 70

⇒ 12x = 60

⇒ x = 5

∴ The correct answer is 5 years.

Additional Information

Age Sum Property

If the sum of ages of 'n' people after 't' years is S, their present sum is S − (n × t).

Ratio Method for Ages

The difference between the ages of two persons remains constant at all points in time.

Base Change in Ages

Always define all members in terms of a single variable (usually the youngest person) to simplify linear equations.

Shortcut Trick

Total Loss = Rs. 3000.

Ratio of loss shared by A and B is 2 : 1.

Total units of loss = 2 + 1 = 3 units.

3 units = Rs. 3000 ⇒ 1 unit = Rs. 1000.

Share of A = 2 units = 2 × 1000 = Rs. 2000.

∴ The correct answer is Rs. 2000.

Alternate Method

Given → Total Loss = Rs. 3000, Ratio of Loss (A:B) = 2:1. Formulas: Share of X = (Ratio of X ÷ Sum of Ratios) × Total Value.

⇒ Let the loss shared by B be x. ⇒ Then, the loss shared by A = 2x. ⇒ Total Loss = 2x + x = 3x. ⇒ 3x = 3000 ⇒ x = 1000. ⇒ Share of A = 2x = 2 × 1000 = Rs. 2000.

∴ The correct answer is Rs. 2000.

Additional Information

Partnership Ratios

In a partnership, profit or loss is generally divided in the ratio of Investment × Time unless a specific condition is mentioned.

Conditional Profit Sharing

Agreements can specify different ratios for Profit and Loss as per the contract between partners.

Nine persons are sitting in a row facing north.

1) A sits immediately right of one who sits fourth from the one of the extreme end. Three people sit between A and G. B sits immediately left of G.

2) D is the only neighbor of B. The number of persons sitting to the right of F is the same as the number of persons sitting to the left of C. 

In Case 2, B has two neighbors which contradicts the condition that D is the only neighbor of B. So, Case 2 is eliminated.

3) The persons between H and C are two less than the persons sitting between E and F. 

The given condition is not satisfied in Case 1(a). So, Case 1 is eliminated. Zero persons are sitting between H and C which is two less than the number of persons(two) sitting between E and F.

4. Peson J will be placed in the remaining position.

The final arrangement is:

 

Hence, One person is sitting to the right of J.

Nine persons are sitting in a row facing north.

1) A sits immediately right of one who sits fourth from the one of the extreme end. Three people sit between A and G. B sits immediately left of G.

2) D is the only neighbor of B. The number of persons sitting to the right of F is the same as the number of persons sitting to the left of C. 

In Case 2, B has two neighbors which contradicts the condition that D is the only neighbor of B. So, Case 2 is eliminated.

3) The persons between H and C are two less than the persons sitting between E and F. 

The given condition is not satisfied in Case 1(a). So, Case 1 is eliminated. Zero persons are sitting between H and C which is two less than the number of persons(two) sitting between E and F.

4. Peson J will be placed in the remaining position.

The final arrangement is:

 

Hence, F sits second to the right of the person who is sitting immediate left of H.

Nine persons are sitting in a row facing north.

1) A sits immediately right of one who sits fourth from the one of the extreme end. Three people sit between A and G. B sits immediately left of G.

2) D is the only neighbor of B. The number of persons sitting to the right of F is the same as the number of persons sitting to the left of C. 

In Case 2, B has two neighbors which contradicts the condition that D is the only neighbor of B. So, Case 2 is eliminated.

3) The persons between H and C are two less than the persons sitting between E and F. 

The given condition is not satisfied in Case 1(a). So, Case 1 is eliminated. Zero persons are sitting between H and C which is two less than the number of persons(two) sitting between E and F.

4. Peson J will be placed in the remaining position.

The final arrangement is:

 

Hence, D is sitting at one of the extreme ends is true statement.

Nine persons are sitting in a row facing north.

1) A sits immediately right of one who sits fourth from the one of the extreme end. Three people sit between A and G. B sits immediately left of G.

2) D is the only neighbor of B. The number of persons sitting to the right of F is the same as the number of persons sitting to the left of C. 

In Case 2, B has two neighbors which contradicts the condition that D is the only neighbor of B. So, Case 2 is eliminated.

3) The persons between H and C are two less than the persons sitting between E and F. 

The given condition is not satisfied in Case 1(a). So, Case 1 is eliminated. Zero persons are sitting between H and C which is two less than the number of persons(two) sitting between E and F.

4. Peson J will be placed in the remaining position.

The final arrangement is:

Hence, Three persons are sitting between G and A.

Nine persons are sitting in a row facing north.

1) A sits immediately right of one who sits fourth from the one of the extreme end. Three people sit between A and G. B sits immediately left of G.

2) D is the only neighbor of B. The number of persons sitting to the right of F is the same as the number of persons sitting to the left of C. 

In Case 2, B has two neighbors which contradicts the condition that D is the only neighbor of B. So, Case 2 is eliminated.

3) The persons between H and C are two less than the persons sitting between E and F. 

The given condition is not satisfied in Case 1(a). So, Case 1 is eliminated. Zero persons are sitting between H and C which is two less than the number of persons(two) sitting between E and F.

4. Peson J will be placed in the remaining position.

The final arrangement is:

Hence, H sits in the middle of the row.

The least possible venn diagram is:

Conclusions-

 

1- Some inks are pencils- False (as it is a possibility but nothing is definite about it).

2- No inks are pencils- False (as it is a possibility but nothing is definite about it).

 

Here conclusion I and II are complementary pairs.

 

Therefore either conclusion I or Conclusion II is true.

The least possible venn diagram is:

Conclusions-

 

1- Some trucks are not jeeps- False (as it is a possibility but nothing is definite about it).

2- All trucks are jeeps- False (as it is a possibility but nothing is definite about it).

 

Here conclusion I and II are complementary pairs.

 

Therefore either conclusion I or Conclusion II is true.