SBI PO Prelims Memory Based Paper (Held on: 21 Nov 2021 Shift 3) (Previous Year Paper)

The correct answer is option 5, i.e. tosspot.

The word ‘tussle’ means ‘a vigorous struggle or scuffle’.

In the above question, the word ‘not’ is written thus, we must select the answer choice that is nowhere close to the given word.

Options 1, 2, 3 and 4 are all synonymous with the given word and thus, can be rejected as our answer choices.

The word has been used in the above passage as, ‘At the heart of its latest tussle (brawl or fight) with the government is India's pervasive problem with spam and nuisance calls’.

Thus, the only option choice that is not relevant with the given word is option 5, i.e. ‘tosspot’ which is used to refer to a habitual drinker (also used as a general term of abuse).

The correct answer is option 3, i.e. two, use of government's anti-spam app.

The answer to the above question can be traced from the introductory paragraph of the above passage.

In the paragraph, it is stated that, ‘For almost two years, Apple has battled India's telecom regulator over a demand that it allow the use of the government's anti-spam app’.

Moreover, the first blank is regarding the number of years thus, option 1 can be rejected on first reading.

Option 5 can also be rejected as in the given context we are referring to single government’s (singular) app and not multiple governments (plural) apps.

Only option 3 captures the correct answer choice, thus it is the only appropriate answer.

The correct answer is option 2, i.e. tariffs.

This is a direct question meaning its answer can be traced directly from the passage and no inference of any sort is required to mark the answer. The answer to the above question can be traced from the last paragraph of the above passage.

In the paragraph, it is clearly stated that, ‘Apple has also failed to find favour with Prime Minister Narendra Modi's administration when it comes to **tariffs (**a tax or duty to be paid on a particular class of imports or exports)’.

Thus, rest of the options can be rejected.

The correct answer is option 3, i.e.Apple – USA &  Xiaomi – China.

Key Points

In the first paragraph of the above passage, it is mentioned that, ‘Local content prerequisites have also stopped the U.S. tech giant from opening its own stores’. Here, ‘U.S. tech giant’ refers to Apple.

In the last paragraph of the above passage, it is mentioned that, ‘A key supplier for China's Xiaomi, another major Apple rival, this week said it would spend $200 million to build a plant in southern India’.

Thus, from both the statements we infer that option 3 is the most appropriate answer choice.

Moreover, we must always look for the most appropriate answer choice (mentioned in question also) which is option 3 and on that basis we can reject options 1 and 2.

The correct answer is option 3, i.e. Xiaomi.

This is probably one of the easiest question of all whose answer can be located from the last paragraph of the passage where it is stated that, ‘A key supplier for China's Xiaomi, another major Apple rival, this week said it would spend $200 million to build a plant in southern India’.

Based on direct reference from the last paragraph, the most appropriate answer choice is option 2.

The correct answer is option 4, i.e. privacy policy of the App Store.

This is a direct question meaning its answer can be traced directly from the passage and no inference of any sort is required to mark the answer. The answer to the above question can be traced from the beginning of the second paragraph of the above passage.

In the paragraph, it is clearly stated that, ‘The app has been available on the Android store since 2016, but Apple in March said that TRAI's app ‘as envisioned violates the privacy policy of the App Store’’.

Thus, rest of the option choice can be rejected.

The correct answer is option 1, i.e. aggravate.

The word ‘exacerbating’ means ‘to make (a problem, bad situation, or negative feeling) worse’.

The word has been used in the above passage as, ‘The steep tariffs are exacerbating (amplifying or intensifying) sales woes for Apple in India, where it has to rely on a network of distributors to supply devices’.

From the given options, both 2 and 3 can be rejected as they are the antonyms of the given word.

Option 4, i.e. ‘exotic’ means ‘originating in or characteristic of a distant foreign country’ and can be rejected as it is irrelevant with the given word.

Option 5, i.e. ‘exquisite’ means ‘extremely beautiful and delicate’ and is also irrelevant with the given word and thus, can be rejected.

Thus, the only correct answer choice is option 1.

The correct answer is option 2, i.e. All except ii, iii and iv, i.e. both i and v follow.

The answer to this question can be traced from the last lines of the second paragraph where it is clearly stated that,

‘We look forward to working with TRAI to address the issue of unsolicited commercial communications, while simultaneously ensuring that we fully honor our commitment to protect the privacy and security of our users’, Apple's head of public policy in India, Kulin Sanghvi, wrote in a letter.

Since, the statements has been said by Kulin Sanghvi who is Apple's head of public policy in India and only option 2 captures both the choices thus it is the most correct answer choice.

R.S. Sharma is TRAI’s Chairman and is not the one who said the given statement thus, ii and iii can be rejected.

Moreover, ‘Apple’s head private policy in India’ is out of context thus, iv can be rejected.

The correct answer is 'Only I and II'.

Key Points

In the given statements, the errors are in statement I and statement II.​

• ​​​In statement I, its should be replaced by it’s (it is) to make the sentence grammatically correct.
• Here Its is a possessive determiner we use to say that something belongs to or refers to something whereas it’s is a contraction of “it is” or “it has”.
• For e.g.- 1. Its been a year since the last time they met. (Incorrect)                          2. It’s been a year since the last time they met. (Correct)
• In statement II, the verb should be say in place of says since the subject is researchers, which is plural in number. According to the Subject-verb Concord, the verb must agree with its subject in number and person.
• For e.g.- No examples are relevant to the case

Thus, the correct sentences are I. It’s hazardous to use a handheld cell phone while driving.  and II. T**hey are also dangerous say, researchers.

Statement III is grammatically and contextually correct. Sentence III is an example of subject-verb agreement with a compound subject.

Additional Information

Compound subjects (two subjects in the same sentence) usually take a plural verb, unless the combination is treated as singular in popular usage or the two subjects refer to the same thing or person.

• Neither my dad nor my brothers know how to ski. (Correct sentence)
• Corn and cheese are great on a pizza. (Correct sentence)

The correct answer is 'Only I and III'.

Key Points

In the given statements, the errors are in statement I and statement III.

• In statement I, the preposition at will be replaced by on to make the sentence grammatically correct. The idiom on the verge of means at the point when (something) is about to happen or is very likely to happen.
• For e.g.- The company was on the verge of going bankrupt.
• In statement III, the preposition in will be replaced by over because the preposition in indicates rest or motion inside anything or refer to a period of time usually in the future.
• For e.g.- She is in the garden.
• He will return in a month

<br>

Here the sentence talks about clouds so we have to use the preposition over which means moving across space above someone or something to make the sentence grammatically correct.

• Statement II is grammatically and contextually correct. Here the preposition by is used which means according to; from the evidence of.
• For e.g.- By my watch, it is 10:30.
• Thus the correct sentences are: I. India’s manufacturing sector was believed to be on the verge of sickness. and **​II. Clouds hung thick and grey over Bengaluru airport.

<br>

Additional Information

Over can be used in the following ways

The correct option is 3) i.e. Worry

Key Points

• Option 3: Worry (verb)- Feel or cause to feel anxious or troubled about actual or potential problems.
• This word fits the blank correctly and conveys the meaning that his three sons were a matter of grave concern(worry) for Amarasakti. It means that King Amarasakti troubled by the action of his sons, this caused him anxiety (worry). ✔️
• Example: He worried about his soldier sons in the war.

​

Additional Information

• Option 1: Joy(noun)- a feeling of great pleasure and happiness. This word does not fit the blank correctly. ❌
• Example: My heart is singing for joy this morning.
• Option 2: ache(noun)- a continuous or prolonged dull pain in a part of one's body. This word does not fit the blank correctly. ❌
• Example: The ache deep within her started again.
• Option 4: Pity(noun)- a feeling of sadness or sympathy for someone else's unhappiness or difficult situation. This word does not fit the blank correctly.❌
• Example: These people don't want pity, they want practical help.
• Option 5: Hazard(noun)- a danger or risk. This word does not fit the blank correctly. ❌
• ​Example: Polluted water sources are a hazard to wildlife.

The correct option is 4) i.e. Realising

Key Points

• Option 4: Realising(verb)- Become fully aware of (something) as a fact, understand clearly. 
• This word fits the blank correctly and conveys the meaning that King Amarasakti has understood that his sons have no interest in learning and therefore will not be able to perform their duties properly towards the subject of the land. ✔️
• Example: He realized his mistake at once.

​

Additional Information

• Option 1: Fact(noun)- a thing that is known or proved to be true. This word does not fit the blank correctly. ❌
• Example: He ignores some historical and economic facts.
• Option 2: Belief(noun)- trust, faith, or confidence in (someone or something). This word does not fit the blank correctly. ❌
• Example: That man has a strong belief in Buddhism.
• Option 3: Since(preposition)- in the intervening period between (the time mentioned) and the time under consideration, typically the present. This word does not fit the blank correctly.❌
• Example: She hasn't spoken to him since last year.
• ​Option 5: Being(noun)- existence. This word does not fit the blank correctly. ❌
• ​Example: The railway brought many towns into being.

The correct option is 2) i.e. fool

Key Points

• Option 2: fool(noun)- a person who acts unwisely or imprudently, a silly person. We use this term to denote a person who has acts in a manner that is considered to be unsuited in a particular circumstance.
• This word fits the blank correctly and the meaning that according to men of learning, an unborn son is better than a son who is a muttonhead (a slang term used to express disapproval).✔️
• Example: I felt like a fool for speaking out of turn in the meeting.

​

Additional Information

• Option 1: great(adjective)- having or showing greatness. ❌
• Example: He was a benevolent man, great and kind.​
• Option 3: brilliant(adjective)- exceptionally clever or talented. This word does not fit the blank correctly.❌
• Example: He was quite brilliant and was promoted almost at once.
• Option 4: disciple(noun)- a follower or pupil of a teacher, leader, or philosopher. This word does not fit the blank correctly. ❌
• Example: Adversity is a good disciple.
• Option 5: scholar(noun)- a specialist in a particular branch of study, especially the humanities. This word does not fit the blank correctly. ❌
• ​Example: He became a good Hungarian scholar.

The correct option is 1) i.e. successors

Key Points

• Option 1: Successors(noun)- a person or thing that succeeds another. It means that the object is next in line to something that is being passed on or passed down. 
• This word does not fit the blank correctly and conveys a proper meaning that how he can make his sons fit to be his heir? ✔️
• Example: Schoenberg saw himself as a natural successor to the German romantic school.

​

Additional Information

       Example: I couldn't entrust my children to strangers.     

• Option 2: self(noun)- a person's essential being that distinguishes them from others, especially considered as the object of introspection or reflexive action. This word does not fit the blank correctly. ❌
• Example: While Molly was her usual quiet self, and perhaps a little nervous, it was obvious she was excited.
• Option 3: place(noun)- a particular position, point, area in space, a location. This word does not fit the blank correctly.❌
• Example: I can't be in two places at once.
• Option 4: level(noun)- a horizontal plane or line with respect to the distance above or below a given point. This word does not fit the blank correctly. ❌
• Example: The front garden is on a level with this floor.
• Option 5: siblings(noun)- a brother or sister. This word does not fit the blank correctly. ❌
• ​Example: I have four siblings: three brothers and a sister.
• ​​Entrust(v erb): put (something) into someone's care or protection

The correct option is 4) i.e. suggested

Key Points

• Option 4: Suggested(Verb)- put forward for consideration. This word does fits the blank correctly and meaning that one of the ministers recommends the name of Vishnu Sharman. 'Suggest' means to give kind advice to an individual, group or organization. ✔️
• • Example: I suggest that we wait a day or two.

​

Additional Information

• Option 1: pointed(adjective)- (of a remark or look) expressing criticism in a direct and unambiguous way. This word does not fit the blank correctly. ❌
• Example: Pointed comments were made about racial discrimination within the army.
• Option 2: called(verb)- cry out. This word does not fit the blank correctly. ❌ 
• Example: He heard an insistent voice calling his name.
• Option 3: requested(verb)- politely or formally ask for. This word does not fit the blank correctly.❌
• Example: He received the information he had requested.
• Option 5: said(verb)- utter words so as to convey information, an opinion, a feeling or intention, or an instruction. This word does not fit the blank correctly. ❌
• ​Example: He became a good Hungarian scholar.
• Summon(verb): order (someone) to be present.
• Example: They were summoned to the court to give advice.

The correct option is 5) i.e. respect

Key Points

• Option 5: Respect(noun)- a feeling of deep admiration for someone or something elicited by their abilities, qualities, or achievements. 
• This word fits the blank correctly and conveys a proper meaning that a great scholar Vishnu Sharman enjoying the popularity of hundreds of his disciples.✔️ 
• ​Example: The director had a lot of respect for Douglas as an actor.

​

Additional Information

• Option 1: rights(adjective)- morally good, justified, acceptable. This word does not fit the blank correctly. ❌
• Example: I want no manly rights for women.
• Option 2: attendance(noun)- the action or state of going regularly to or being present at a place or event. This word does not fit the blank correctly. ❌
• Example: My attendance at church was very patchy.
• Option 3: glamour(noun)- an attractive, exciting quality that makes certain people or things seem appealing. This word does not fit the blank correctly.❌
• Example: She left her hometown, attracted to the glamour of the big city.
• Option 4: teachings(noun)- the occupation, profession, or work of a teacher. This word does not fit the blank correctly. ❌
• Example: I went into teaching because I like working with children.
• Witless(adjective): foolish, stupid.
• Example: The novel centers around a witless father who is continually being conned by his three children.

The correct option is 1) i.e. competent

Key Points

• Option 1: Competent(adjective)- (of a person) efficient and capable. Also used in official purposes where we say that the signature of 'competent' authority is required, meaning that the concerned person will be responsible for after signing a particular document. 
• This word fits the blank correctly and conveys a proper meaning that he (Vishnu Sharman) is the most capable person to tutor the king's children.✔️
• Example: An infinitely competent mother of three.

​​​

Additional Information

• Option 2: right(adjective)- morally good, justified, acceptable. This word does not fit the blank correctly. ❌ 
• Example: I hope we're doing the right thing.
• Option 3: easy(adjective)- achieved without great effort, presenting few difficulties. This word does not fit the blank correctly.❌
• Example: You make an easy target.
• Option 4: actual(adjective)- existing in fact, real. This word does not fit the blank correctly. ❌
• Example: The estimate was much less than the actual cost.
• Option 5: skill(noun)- the ability to do something well; expertise. This word does not fit the blank correctly. ❌
• ​Example: We have the skill and the strategy.

The correct answer is Only II**.**

Key Points

In the given statements, the error is in statement II where by will replace with because by is used to denote the doer of an action/object in the Passive Voice.

Here the doer of an action/object is 'his friend'.

• For e.g.- The thief was beaten by a policeman.

<br>

The preposition 'With' means ‘in the same place as someone or something or ‘accompanying’.

• ​​For e.g.- He struck the dog with a stick.
• Statement I doesn't have any error because the usage of 'No sooner...than' is correct. Whenever we use the adverb 'no sooner' at the starting of the sentence, it is always followed by a helping verb.
• Statement III is correct because here the usage of won’t is grammatically correct. Here Won’t implies that you are choosing not to do something, whether or not you have the ability.

Thus, the correct sentence is: The patient was accompanied by his friend.

Additional Information

Whenever adverbs like “No sooner”, “Hardly”, “Scarcely”, etc. are used at the beginning of a sentence, they are always followed by a helping verb.

• Hardly had I begun to speak when I was interrupted.
• ​Scarcely had we started our meal when the phone rang.​

​​

 

 Note that adverbs “hardly, scarcely, and barely” are always followed by “when”, while “No sooner” is followed by “than”.

The correct answer is Option 2 i.e., Both I and II.

 

• These are conditional sentences, and in these types of sentences, one part of the sentence depends upon the other because of cause and effect.

Part I-

• Part I is a First Conditional sentence, and hence follows rule number ‘1’.

• According to this rule**,** the error lies in the wrong usage of ‘may not implemented’ in the main clause.

• Hence, ‘may not implemented’ should be replaced by ‘may not implement’ to make the sentence correct.

• Let’s see an example-

• If Stefan comes to my party, I will give him a surprise. 

• If Stefan comes to my party, I will gave him a surprise. 

Part II-

• Part II follows rule number ‘4’.

• According to the rule**,** the error lies in the wrong usage of ‘will join’ in the main clause.

• Hence, ‘will join’ should be replaced by ‘would have joined’ to make the sentence correct.

• Let’s see an example-

• Had I watched that movie, I would have participated in the discussion. 

• Had I watched that movie, I will participate in the discussion. 

• In the given sentence, ‘will join’ is wrongly used instead of ‘would have joined’ in the main clause.

 

So, the correct sentences are:

Correct sentence I: “If Bangladesh follows the Paris Climate Agreement, the country may not implement other projects such as Rampal Power Plant and Rooppur nuclear power plant.” 

Correct sentence II: “Had he completed the assignment on time, he would have joined us on the trip to Goa.” 

 

• Conditional sentences follow a special structure.
• Conditional words are If, until, unless, as soon as, when, while, as long as, since, etc.

The correct answer is A - B.

Key Points

Let us look at the given sentence in the following manner: 

• Since I live in a ______(A) region, I ______(B) all of the seasons from ______(C) summers to _____(D) winters.
• From the below-given table, we get to know the meanings of the words in bold.
• In (A) experience region and in (B) I temperate both are incorrect phrases.
• The sentence tells us that she lives in a region where she can experience all of the seasons from warm summers to cold winters.
• So, A and B should be interchanged to make the sentence correct. 
  

Therefore the correct sentence is, ***Since I live in a temperate region, I experience all of the seasons from warm summers to cold winters.***​

Additional Information

To understand which word belongs to which blank we need to know their meanings as enlisted below:

The correct answer is C - B. 

Key Points

Let us look at the given sentence in the following manner*:*

• ______(A) many people today, I ______(B) a _____(C) book made out of paper over an electronic _____(D) tool.
• From the below-given table, we get to know the meanings of the words in bold.
• In (C) a prefer book and in (B) I tangible both are incorrect phrases.
• The sentence tells us that she prefers a physical book rather than an electronic book.
• So, C and B should be interchanged to make the sentence correct. 
  

Therefore the correct sentence is, Unlike many people today, I prefer a tangible book made out of paper to an electronic reading tool. ​

Additional Information

To understand which word belongs to which blank we need to know their meanings as enlisted below:

The correct answer is B-A.

Key Points

Let us look at the given sentence in the following manner: 

• Two teens were ________ (A) with ________ (B) after they ________ (C) painted curse words on their elderly neighbour’s ________ (D).
• From the below-given table, we get to know the meanings of the words in bold.
• In (B) with charged and in (A) were vandalism both are incorrect phrases.
• The sentence tells us that two teens were accused of damaging an elderly neighbour’s garage with spray-painted curse words.
• So, B and A should be interchanged to make the sentence correct. 
  

Therefore the correct sentence is, Two teens were charged with vandalism after they spray-painted curse words on their elderly neighbour’s garage.

​

Additional Information

To understand which word belongs to which blank we need to know their meanings as enlisted below:

The correct answer is B-C.

Key Points

Let us look at the given sentence in the following manner: 

• When Jim did not get the ________ (A) he thought he ________ (B) in court, he got his own ________ (C) by ________ (D) his attack.
• From the below-given table, we get to know the meanings of the words in bold.
• In (B) he vengeance and in (C) his own deserved both are incorrect phrases.
• The sentence tells us that Jim got his vengeance when he thought he did not get the correct justice in court.
• So, B and C should be interchanged to make the sentence correct. 
  

Therefore the correct sentence is, When Jim did not get the justice he thought he deserved in court, he got his own vengeance by shooting his attack.

​

Additional Information

To understand which word belongs to which blank we need to know their meanings as enlisted below:

The correct answer is 'All A, B, and C'.

Key Points

• Instant means happening suddenly or immediately.
• Example- The film was an instant success.
• All 3 sentences have been used correctly.
• Hence. the correct answer is option 4.

The correct answer is 'Only A and B'.

Key Points

• Only sentences A and B express the correct meanings of the word dock.
• In sentence C the word dock is incorrect.
• The correct word should be 'honest' in place of dock.
• Dock means an area of a port where ships stop to be loaded, repaired, etc. (गोदी, बंदरगाह का वहा हिस्‍सा जहाँ जहाज़ का माल उतारा-चढ़ाया जाता है, जहाज़ की मरम्‍मत होती है आदि )
• Hence, sentence A and B gives appropriate meaning.
• Hence, the correct answer is option 4.

The correct answer is Only B

Key Points

• Let's look at the meaning of the word:
• Denouement:  the final part of a play, movie, or narrative in which the strands of the plot are drawn together and matters are explained or resolved
• The first sentence states that there is no 'progress' in the plan, this refers to the movement of a plan from start to finish but this means that the plan is not at its final stage yet. 
• Also, since there is mention only of one plan, it would have only one 'denouement' (singular).
• The third sentence refers to a condition being 'denouement', whereas 'denouement' is not a state one can achieve.
• The second sentence mentions a 'story' and how the speaker does not want to 'ruin' it, ruining a story would usually work by revealing the ending, thus defeating the whole purpose of indulging in the story in the first place.

<br>

Thus, the correct answer is Only B.

The correct answer is Both B and C.

Key Points

The meaning of ‘ephemeral’ is lasting for a very short time. It is an adjective.

• In sentence A, ephemeral is inappropriately used. It should be replaced with perennial to make the sentence contextually correct.
• In sentence B, the word has been correctly used. Here the word ephemeral is aptly used as it is used for denoting the time period of newly coined words.
• In sentence C, ephemeral means ‘lasting for a very short time. So it fits the context perfectly where the word is used to describe one of the types of the lake. One lasting for a short span of time and the other forever.

Additional Information                                   

The correct answer is Bolsters.

Key Points

• Impact(Noun): A forceful consequence; a strong effect
• Ex: "the book had an important impact on my thinking"
• Bolsters(V): Support and strengthen
• Ex: "Bolster morale"
• Hence, the word Impact should be replaced with the word Bolsters to form a contextually correct sentence.

It should read as: He might lose a sense of his superiority which bolsters his ego in public and private life.differently.​

Additional Information

Let us understand the meaning of other words.

• Bear(V): Have as a feature; convey
• "Bear a signature"
• Boosted(V): to increase something in number, value or strength
• "If we lower the price, that should boost sales."
• Candour(Noun): the trait of being honest and frank.
• "I admire her candour, especially when nobody else bothers to speak up."
• Tolerate(V): Put up with something or somebody unpleasant
• "he learned to tolerate the heat"

The correct answer is the people reached Mumbai when.

Key Points

• There are two errors in the bold part.
• Firstly, the term ‘people’ is a collective noun. Collective nouns are used in the singular form. Therefore, ‘peoples’ must be replaced by ‘people’ in order to make the sentence correct.
• Secondly, ‘hardly’ and ‘when’ form a pair of coordinating conjunctions. Coordinating conjunctions join phrases, words, etc. of equal ranks. Therefore, ‘when’ should be used instead of ‘than’ in order to make it a grammatically correct sentence.
• Among the choices available, option 3 replaces the bold part most appropriately.
• Hence, option 3 is the correct answer.

The correct sentence is: Hardly had the people reached Mumbai when they were ordered to return to Delhi.

Additional Information

• Hardly -when is used in past perfect tense sentences as follows. Sometimes we use Scarcely-when in place of Hardly-when
• Hardly had the race started when we started cheering.
• Scarcely had you asked a question when he answered it.
• We can use 'no sooner- than' as follows.
• No sooner did we call him than he responded.

The correct answer is A - B. 

Key Points

Let us look at the given sentence in the following manner: 

• After ______(A) a low _______(B) on my diamond ring, I realized the ______(C) looking jeweller had sold me a ______(D) jewel.
• From the below-given table, we get to know the meanings of the words in bold.
• In (A) after appraisal and in (B) low receiving both are incorrect phrases.
• The sentence tells us that she received a very low consideration for her diamond ring that made her realize that the suspicious-looking jeweller might have sold her a fake jewel.
• So, A and B should be interchanged to make the sentence correct. 
  

Therefore the correct sentence is, ***After receiving a low appraisal on my diamond ring, I realized the suspicious-looking jeweller had sold me a spurious jewel.***​

Additional Information

To understand which word belongs to which blank we need to know its meaning as enlisted below:

Calculation:

l. 24x² + 38x + 15 = 0

⇒ 24x² + 18x + 20x + 15 = 0

⇒ 6x(4x + 3) + 5(4x + 3) = 0

⇒ (6x + 5) (4x + 3) = 0

⇒ x = -5/6, -3/4

ll. 54y² + 123y + 65 = 0

⇒ 54y² + 78y + 45y + 65 = 0

⇒ 6y(9y + 13) + 5(9y + 13) = 0

⇒ (6y + 5) (9y + 13) = 0

⇒ y = -5/6, -13/9

Comparison between x and y (via Tabulation):

 

∴ The result will be x ≥ y.

First Equation:

x² + 36x + 243 = 0

⇒ x² + 27x + 9x + 243 = 0

⇒ x(x + 27) + 9(x + 27) = 0

⇒ (x + 27)(x + 9) = 0

⇒ x = -27 or x = -9

Second Equation:

2y² – 32y + 120 = 0

⇒ 2y² – 12y – 20y + 120 = 0

⇒ 2y(y – 6) – 20(y – 6) = 0

⇒ (y – 6)(2y – 20) = 0

⇒ y = 6 or y = 10

Comparison between x and y (via Tabulation):

<br>

∴ y > x

Calculations:

I. 24x² + 96x + 90 = 0

⇒ 6(4x² + 16x + 15) = 0

⇒ 4x² + 16x + 15 = 0

⇒ 4x² + 10x + 6x + 15 = 0

⇒ 2x(2x + 5) + 3(2x + 5) = 0

⇒ (2x + 5) (2x + 3) = 0

⇒ x = -5/2, -3/2

 

II. 28y² + 56y + 21 = 0

⇒ 7(4y² + 8y + 3) = 0

⇒ 4y² + 8y + 3 = 0

⇒ 4y² + 6y + 2y + 3 = 0

⇒ 2y(2y + 3) + 1(2y + 3) = 0

⇒ (2y + 3)(2y + 1) = 0

⇒ y = -3/2, -1/2

 

 

∴ x ≤ y

I. x² + 3x – 130 = 0 

⇒ x² + 13x – 10x – 130 = 0

⇒ x(x + 13) – 10(x + 13) = 0

⇒ (x – 10) (x + 13) = 0

⇒ x = 10, -13

II. 2y² – 10y – 208 = 0 

⇒ y² – 5y – 104 = 0

⇒ y² – 13y + 8y – 104 = 0

⇒ y(y – 13) + 8(y – 13) = 0

⇒ (y + 8) (y – 13) = 0

⇒ y = -8, 13

 

∴ x = y or the relationship between x and y cannot be established.

As constant terms of both the equations are negative, we can say the answer will be 'relationship between x and y cannot be established'.

I.) 2x2 – 3x – 2 = 0

⇒ 2x² – 4x + x – 2 = 0

⇒ 2x(x – 2) + 1(x – 2) = 0

⇒ (2x + 1) (x – 2) = 0

⇒ x = -1/2, 2

II. 4y2 – 17y + 4 = 0

⇒ 4y² – 16y – y + 4 = 0

⇒ 4y(y – 4) – 1(y – 4) = 0

⇒ (4y – 1) (y – 4) = 0

⇒ y = 1/4, 4

 

 

∴ x = y or relationship between x and y cannot be established

6

⇒ 6 × 1 - 1 = 5

⇒ 5 × 2 - 2 = 8

⇒ 8 × 3 - 3 = 21

⇒ 21 × 4 - 4 = 80

⇒ 80 × 5 - 5 = 395

∴ 81 is the wrong in the given pattern

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.

Given:

32, 33, 25, 52, 12, 113

Calculation:

The series follows the following pattern,

32 + 1³ = 33

33 - 2³ = 25

25 + 3³ = 52

52 - 4³ = -12 ≠ 12

-12 + 5³ = 113 

Since -12 will come in place of 12.

∴ The required wrong number will be 12.

Given:

12, 6, 24, 3, 44, 1.5

Calculation:

The series follows the following pattern,

12 ÷ 2 = 6

6 × 4 = 24

24 ÷ 8 = 3

3 × 16 = 48 ≠ 44

48 ÷ 32 = 1.5

Since 48 will come in place of 44

∴ The required wrong number will be 44.

Given:

429, 436, 447, 452, 481, 504

Calculation:

The pattern of the given series can be explained as,

Since 462 will come in place of 452

∴ The required wrong number will be 452.

Given:

Ratio of Boys to Girls who participate in Dancing = 4 : 3

Ratio of Boys to Girls who participate in Singing = 8 : 13

Ratio of Boy to Girl who participates in both the events of Singing and Dancing = 2 : 1

Ratio of Boys to Girls who participate only in the Singing event = 1 : 2

participation of boys in the Dancing event alone is 10 more than the Girls participation in Dancing alone

Boys who participate in both Dancing and Singing is 20% of the Boys who participate in Dancing events alone

Concept:

Total participant in Dance = participate only in Dance + participate in both Dancing and Singing

Total participant in Singing = participate only in Singing + participate in both Dancing and Singing

Calculation:

Let number of Girl participate only in dancing = x

So, Number of Boys participate only in dancing = x + 10

Number of Boys participate in both Dancing and Singing = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both Dancing and Singing = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in dance/Number of girls participate in dance = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in dancing = 40

Number of Boys participate only in dancing = 40 + 10

⇒ 50

Number of Boys participate in both Dancing and Singing = (40 + 10)/5

⇒ 10

Number of Girls participate in both Dancing and Singing = (40 + 10)/10

⇒ 5

Number of participants who participated in both events (Dancing and Singing) = 10 + 5

⇒ 15

∴ 15 participants, participated in both events (Dancing and Singing).

Given:

Ratio of Boys to Girls who participate in Dancing = 4 : 3

Ratio of Boys to Girls who participate in Singing = 8 : 13

Ratio of Boy to Girl who participates in both the events of Singing and Dancing = 2 : 1

Ratio of Boys to Girls who participate only in the Singing event = 1 : 2

participation of boys in the Dancing event alone is 10 more than the Girls participation in Dancing alone

Boys who participate in both Dancing and Singing is 20% of the Boys who participate in Dancing events alone

Concept:

Total participant in Dance = participate only in Dance + participate in both Dancing and Singing

Total participant in Singing = participate only in Singing + participate in both Dancing and Singing

Calculation:

Let number of Girl participate only in dancing = x

So, Number of Boys participate only in dancing = x + 10

Number of Boys participate in both Dancing and Singing = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both Dancing and Singing = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in dance/Number of girls participate in dance = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in dancing = 40

Number of Boys participate only in dancing = 40 + 10

⇒ 50

Number of Boys participate in both Dancing and Singing = (40 + 10)/5

⇒ 10

Number of Girls participate in both Dancing and Singing = (40 + 10)/10

⇒ 5

Number of Boys participate in dance = 50 + 10

⇒ 60

Number of girls participate in dance = 40 + 5

⇒ 45

Number of Boys in singing/Number of Girls in singing = 8/13

8/13 = (10 + y)/(5 + 2y)

⇒ 40 + 16y = 130 + 13y

⇒ 3y = 90

⇒ y = 30

Let number of Boys who participated only in Singing events is x% of Boys who participated only in Dancing events

x% = (30/50) × 100

⇒ 60%

∴ Number of Boys who participated only in Singing events is 60% of Boys who participated only in Dancing events.

Given:

Ratio of Boys to Girls who participate in Dancing = 4 : 3

Ratio of Boys to Girls who participate in Singing = 8 : 13

Ratio of Boy to Girl who participates in both the events of Singing and Dancing = 2 : 1

Ratio of Boys to Girls who participate only in the Singing event = 1 : 2

participation of boys in the Dancing event alone is 10 more than the Girls participation in Dancing alone

Boys who participate in both Dancing and Singing is 20% of the Boys who participate in Dancing events alone

Concept:

Total participant in Dance = participate only in Dance + participate in both Dancing and Singing

Total participant in Singing = participate only in Singing + participate in both Dancing and Singing

Calculation:

Let number of Girl participate only in dancing = x

So, Number of Boys participate only in dancing = x + 10

Number of Boys participate in both Dancing and Singing = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both Dancing and Singing = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in dance/Number of girls participate in dance = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in dancing = 40

Number of Boys participate only in dancing = 40 + 10

⇒ 50

Number of Boys participate in both Dancing and Singing = (40 + 10)/5

⇒ 10

Number of Girls participate in both Dancing and Singing = (40 + 10)/10

⇒ 5

Number of Boys participate in dance = 50 + 10

⇒ 60

Number of girls participate in dance = 40 + 5

⇒ 45

Number of Boys in singing/Number of Girls in singing = 8/13

8/13 = (10 + y)/(5 + 2y)

⇒ 40 + 16y = 130 + 13y

⇒ 3y = 90

⇒ y = 30

Number of Boys in singing only = 30

Number of Girls in singing only = 2 × 30

⇒ 60

Number of Boys in singing = 30 + 10

⇒ 40

Number of Girls in singing = 60 + 5

⇒ 65

Ratio of boy who participated in Dancing to Girls who participated in Singing = 60 : 65

⇒ 12 : 13

∴ Ratio of boy who participated in Dancing to Girls who participated in Singing is 12 : 13.

Given:

Ratio of Boys to Girls who participate in Dancing = 4 : 3

Ratio of Boys to Girls who participate in Singing = 8 : 13

Ratio of Boy to Girl who participates in both the events of Singing and Dancing = 2 : 1

Ratio of Boys to Girls who participate only in the Singing event = 1 : 2

participation of boys in the Dancing event alone is 10 more than the Girls participation in Dancing alone

Boys who participate in both Dancing and Singing is 20% of the Boys who participate in Dancing events alone

Concept:

Total participant in Dance = participate only in Dance + participate in both Dancing and Singing

Total participant in Singing = participate only in Singing + participate in both Dancing and Singing

 

Calculation:

Let number of Girl participate only in dancing = x

So, Number of Boys participate only in dancing = x + 10

Number of Boys participate in both Dancing and Singing = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both Dancing and Singing = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in dance/Number of girls participate in dance = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in dancing = 40

Number of Boys participate only in dancing = 40 + 10

⇒ 50

Number of Boys participate in both Dancing and Singing = (40 + 10)/5

⇒ 10

Number of Girls participate in both Dancing and Singing = (40 + 10)/10

⇒ 5

Number of Boys participate in dance = 50 + 10

⇒ 60

Number of girls participate in dance = 40 + 5

⇒ 45

Number of Boys in singing/Number of Girls in singing = 8/13

8/13 = (10 + y)/(5 + 2y)

⇒ 40 + 16y = 130 + 13y

⇒ 3y = 90

⇒ y = 30

Number of Boys in singing only = 30

Number of Girls in singing only = 2 × 30

⇒ 60

Participant only in Dancing = 50 + 40

⇒ 90

Participant only in Singing = 30 + 60

⇒ 90

Participant only in Dancing : Participant only in Singing = 90 : 90

⇒ 1 : 1

∴ Ratio of participants who participated only in Dancing to only in Singing is 1 : 1.

Given:

Ratio of Boys to Girls who participate in Dancing = 4 : 3

Ratio of Boys to Girls who participate in Singing = 8 : 13

Ratio of Boy to Girl who participates in both the events of Singing and Dancing = 2 : 1

Ratio of Boys to Girls who participate only in the Singing event = 1 : 2

participation of boys in the Dancing event alone is 10 more than the Girls participation in Dancing alone

Boys who participate in both Dancing and Singing is 20% of the Boys who participate in Dancing events alone

Concept:

Total participant in Dance = participate only in Dance + participate in both Dancing and Singing

Total participant in Singing = participate only in Singing + participate in both Dancing and Singing

Total participant in competition = participate only in Dance + participate in both Dancing and Singing + participate only in Singing

Calculation:

Let number of Girl participate only in dancing = x

So, Number of Boys participate only in dancing = x + 10

Number of Boys participate in both Dancing and Singing = (20/100) × (x + 10)

⇒ (x + 10)/5

Number of Girls participate in both Dancing and Singing = (1/2) × {(x + 10)/5}

⇒ (x + 10)/10

Number of Boys participate in dance/Number of girls participate in dance = 4/3

4/3 = {(x + 10) + (x + 10)/5}/{x + (x + 10)/10}

⇒ 2/3 = (6x + 60)/(11x + 10)

⇒ 18x + 180 = 22x + 20

⇒ 4x = 160

⇒ x = 40

Number of Girl participate only in dancing = 40

Number of Boys participate only in dancing = 40 + 10

⇒ 50

Number of Boys participate in both Dancing and Singing = (40 + 10)/5

⇒ 10

Number of Girls participate in both Dancing and Singing = (40 + 10)/10

⇒ 5

Number of Boys participate in dance = 50 + 10

⇒ 60

Number of girls participate in dance = 40 + 5

⇒ 45

Number of Boys in singing/Number of Girls in singing = 8/13

8/13 = (10 + y)/(5 + 2y)

⇒ 40 + 16y = 130 + 13y

⇒ 3y = 90

⇒ y = 30

Number of Boys in singing only = 30

Number of Girls in singing only = 2 × 30

⇒ 60

Number of Boys in singing = 30 + 10

⇒ 40

Number of Girls in singing = 60 + 5

⇒ 65

Total participant in competition = (50 + 40) +(10 + 5) + (30 + 60)

⇒ 90 + 15 + 90

⇒ 195

∴ Total 195 participants were there in the competition.

Total number of votes received by A = 26% of 7000 = 1820

Invalid votes = 200

Valid votes = 1820 – 200 = 1620

∴ Percentage of valid votes = (1620/7000) × 100 = 23.14% ≈ 23%

Valid votes received by A = 1620

Total votes received by C = 18% of 7000 = 1260

∴ Required percentage = [(1620 – 1260) /1260] × 100 = 28.57%

Total votes received by B = 42% of 7000 = 2940

Valid votes received by B = 2940 – 100 = 2840

Total votes received by D = 14% of 7000 = 980

Valid votes received by D = 980 – 120 = 860

Required ratio = 2840 ∶ 860 = 142 ∶ 43

Number of votes received by A, C and D together = 58% of 7000 = 4060

Number of valid votes received by A, C and D together = 4060 – 570 = 3490

Number of votes received by B = 42% of 7000 = 2940

Number of valid votes received by B = 2940 – 100 = 2840

∴ Required difference = 3490 – 2840 = 650

Total number of invalid votes = 200 + 100 + 250 + 120 = 670

∴ Required percentage = (670/7000) × 100 = 9.57%

Number of Computer books sold by A = 20% of 450000 = (20/100) × 4,50,000 = 90,000

Similarly, Number of Computer books sold by B = (10/100) × 5,20,000 = 52,000

Total Computer books sold by both stores together = 90000 + 52000 = 1,42,000

Given that, out of these 1,42,000 Computer books, 15% of the books are returned by the customers.

∴ Number of Computer books originally sold by these stores = 85% of 1,42,000

= (85/100) × 1,42,000 = 120700

Mathematics Books sold by B = Mathematics Books sold by A

∵ Mathematics Books sold by A = 15% of 450000

= (15/100) × 450000 = 67500

∴ Mathematics Books sold by B = 67500

Also, total sold books by B = 520000

∴ Percentage share of Mathematics Books in total sold books by B

= (67500/520000) × 100 = 12.98 ≈ 13%.

Total number of Physics books sold by A = (30/100) × 4,50,000 = 1,35,000

Total number of Physics books sold by B = (25/100) × 5,20,000 = 1,30,000

∴ The difference in Physics books sold by A and B = 1,35,000 – 1,30,000 = 5,000

 

∴ Difference of books sold by store A and B is maximum for English books.

Given: 

Percentage of Chemistry books sold by B = Percentage of Chemistry books sold by A

Percentage of Chemistry books sold by A = 25%

Percentage of Chemistry books sold by B = 25%

∴ Number of Chemistry books sold by B = 25% of 520000 = (25/100) × 520000 = 130000

Shortcut Trick

Apply Alligation: Difference between Male (12000) and Mean (11600) is 400.

Difference between Female (11200) and Mean (11600) is 400.

Ratio of Male : Female = 400 : 400 = 1 : 1.

Female % = 1 ÷ (1 + 1) × 100 = 50%.

∴ The correct answer is 50%.

Alternate Method

Given: Average Male Salary = ₹12000, Average Female Salary = ₹11200, Mean Salary = ₹11600.

Formula Used: Alligation method or Weighted Average formula.

⇒ Ratio of Male : Female = (11600 − 11200) : (12000 − 11600)

⇒ Ratio = 400 : 400

⇒ Ratio = 1 : 1

⇒ Percentage of Female employees = [Female Ratio ÷ (Male Ratio + Female Ratio)] × 100

⇒ Percentage = [1 ÷ (1 + 1)] × 100 = (1 ÷ 2) × 100

⇒ Percentage = 50%

∴ The correct answer is 50%.

Additional Information

Alligation Rule

It is a rule used to find the ratio in which two ingredients at given prices must be mixed to produce a mixture at a given price. Ratio = (Cheaper Quantity) : (Dearer Quantity) = (D − M) : (M − C).

Weighted Average

The mean salary can also be found using Average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂), where n is the count and x is the individual average.

Shortcut Trick

Total workers = 6000

Total male workers = 80% of 6000 = 4800

Male workers below 55 years = (100% − 19%) of Total males

⇒ 81% of 4800 = 81 × 48 = 3888

∴ The correct answer is 3888.

Alternate Method

Given:

Total number of workers = 6000

Percentage of male workers = 80%

Percentage of male workers ≥ 55 years = 19%

Calculations:

⇒ Number of male workers = 6000 × (80/100) = 4800

⇒ Percentage of male workers below 55 years = 100% − 19% = 81%

⇒ Number of male workers below 55 years = 4800 × (81/100)

⇒ 48 × 81 = 3888

∴ The correct answer is 3888.

Additional Information

Percentage Base Change

When calculating a percentage of a subset, first find the subset value: Subset = Total × (Sub% / 100), then apply the second percentage to this result.

Complementary Percentage

If x% of a group belongs to Category A, then (100 − x)% belongs to Category B, provided there are only two mutually exclusive categories.

Shortcut Trick

Initial total ratio sum = 2 + 3 + 4 = 9 units.

Mistaken total ratio sum = 7 + 2 + 5 = 14 units.

Equating total sum (LCM of 9 and 14 = 126): Initial Sita = (3/9) × 126 = 42; Mistaken Sita = (2/14) × 126 = 18.

Difference in Sita share = 42 − 18 = 24 units → ₹60.

Total amount = (60 ÷ 24) × 126 = 2.5 × 126 = ₹315.

∴ The correct answer is ₹315.

Alternate Method

Given: Initial ratio of Radha, Sita, Ram = 2 : 3 : 4. Mistaken ratio = 7 : 2 : 5. Difference in Sita share = ₹60.

Formula Used: Share of a person = (Individual ratio ÷ Total ratio) × Total Amount.

⇒ Let the total amount be x.

⇒ Initial share of Sita = (3 ÷ 9) × x = x/3

⇒ Mistaken share of Sita = (2 ÷ 14) × x = x/7

⇒ Difference = x/3 − x/7 = 60

⇒ (7x − 3x) ÷ 21 = 60

⇒ 4x ÷ 21 = 60

⇒ 4x = 1260

⇒ x = 315

∴ The correct answer is ₹315.

Additional Information

Ratio Balancing

When the same quantity is distributed in two different ratios, multiply the ratios by the sum of the other ratio to equalize the total parts.

Compound Ratio

The compound ratio of (a : b) and (c : d) is (ac : bd). Useful when comparing multiple distribution changes.

Invertendo and Alternendo

If a : b = c : d, then b : a = d : c (Invertendo) and a : c = b : d (Alternendo).

Shortcut Trick

Rahul's present age = 72 − 16 = 56 years.

Tina's age = 56 − 10 = 46 years (given as 23 units).

∴ 1 unit = 46 ÷ 23 = 2 years.

Jatin − Tina = Rahul 4 years ago = 56 − 4 = 52 years.

Jatin's age = 46 + 52 = 98 years.

Value of p = 98 ÷ 2 = 49.

∴ The correct answer is 49.

Alternate Method

Given: Ratio of Tina to Jatin = 23 : p

⇒ Rahul's age after 16 years = 72 years

⇒ Rahul's present age = 72 − 16 = 56 years

⇒ Tina's present age = Rahul − 10 = 56 − 10 = 46 years

⇒ Since 23 units = 46 years, then 1 unit = 2 years

⇒ Jatin − Tina = Rahul's age 4 years ago = 56 − 4 = 52 years

⇒ Jatin's age = 46 + 52 = 98 years

⇒ p = Jatin's age ÷ 1 unit value = 98 ÷ 2 = 49

∴ The correct answer is 49.

Additional Information

Ratio and Proportion in Ages

If the ratio of ages is a : b and the value of one part is 'x', then actual ages are ax and bx.

Age Difference Constant

The difference between the ages of two persons remains constant throughout their lives, regardless of the number of years passed or preceding.

Present Age Calculation

To find the present age from a future age (n years later), subtract n. To find it from a past age (n years ago), add n.

Shortcut Trick

Effective Rate for Simple Interest (SI) = 15% × 2 = 30%.

Effective Rate for Compound Interest (CI) = 6 + 6 + (6 × 6)/100 = 12.36%.

Profit percentage = 30% − 12.36% = 17.64%.

Total Profit = 17.64% of ₹60,000 = 0.1764 × 60,000 = ₹10,584.

∴ The correct answer is ₹10,584.

Alternate Method

Given: Principal (P) = ₹60,000, CI Rate (R₁) = 6%, SI Rate (R₂) = 15%, Time (T) = 2 years.

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

⇒ Simple Interest earned from Nikul = (60,000 × 15 × 2) ÷ 100 = ₹18,000.

⇒ Compound Interest paid to Surya = 60,000[(1 + 6/100)² − 1]

⇒ CI = 60,000[(1.06)² − 1] = 60,000[1.1236 − 1] = 60,000 × 0.1236 = ₹7,416.

⇒ Prashant profit = Interest Received − Interest Paid

⇒ Profit = 18,000 − 7,416 = ₹10,584.

∴ The correct answer is ₹10,584.

Additional Information

Effective Rate of Compound Interest

For a 2-year period, the effective CI rate can be calculated using the successive percentage formula: R + R + (R×R)/100.

Difference between CI and SI

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

Transaction Profit Logic

In lending transactions, profit is the numerical difference between the total interest earned from the borrower and total interest paid to the lender.

Shortcut Trick

Daughter + Son complete full work in (14/3) × (10/7) = 20/3 days.

Daughter + Son + Mother complete full work in 2 × 2 = 4 days.

Using Work = Efficiency × Time, let Total Work = 20 units (LCM of 20/3 and 4).

Efficiency (D+S) = 20 ÷ (20/3) = 3; Efficiency (D+S+M) = 20 ÷ 4 = 5.

Efficiency (Mother) = 5 − 3 = 2 units/day. Time = 20 ÷ 2 = 10 days.

∴ The correct answer is 10 days.

Alternate Method

Given:

Time taken by Daughter (D) + Son (S) for 7/10 work = 14/3 days.

Time taken by D + S + Mother (M) for 1/2 work = 2 days.

Calculations:

⇒ Full work time (D+S) = (14/3) ÷ (7/10) = (14/3) × (10/7) = 20/3 days.

⇒ Full work time (D+S+M) = 2 ÷ (1/2) = 4 days.

⇒ Total Work (LCM of 20/3 and 4) = 20 units.

⇒ Efficiency of Mother = Efficiency (D+S+M) − Efficiency (D+S)

⇒ Efficiency of Mother = 5 − 3 = 2 units/day.

⇒ Time taken by Mother alone = Total Work ÷ Mother Efficiency

⇒ Time = 20 ÷ 2 = 10 days.

∴ The correct answer is 10 days.

Additional Information

Total Work Formula

If a person completes a fraction x/y of work in T days, the time for full work is T × (y/x).

Efficiency Relationship

Combined efficiency of multiple people is the sum of their individual efficiencies (Work/Time).

Time and Work Inverse Rule

Time taken to complete work is inversely proportional to the efficiency: T = W ÷ E.

Shortcut Trick

Cost Price (CP) of mixture = Selling Price (SP) ÷ (1 + Profit%) = 121 ÷ 1.1 = ₹110.

Apply Alligation between ₹150 and ₹100 to get the mean value ₹110.

Ratio = (110 − 100) : (150 − 110) = 10 : 40 = 1 : 4.

∴ The correct answer is 1 : 4.

Alternate Method

Given: CP of Pulse 1 = ₹150/kg, CP of Pulse 2 = ₹100/kg, SP of Mixture = ₹121/kg, Profit = 10%.

Formula Used: CP = [SP × 100] / [100 + Profit%]

⇒ Mean CP of Mixture = (121 × 100) / 110

⇒ Mean CP = ₹110/kg

⇒ Using Rule of Alligation: (Quantity of Pulse 1) / (Quantity of Pulse 2) = (110 − 100) / (150 − 110)

⇒ Ratio = 10 / 40

⇒ Ratio = 1 : 4

∴ The correct answer is 1 : 4.

Additional Information

Rule of Alligation

It is used to find the ratio in which two ingredients at given prices must be mixed to produce a mixture of a specified price. Ratio = (Cheaper CP − Mean CP) : (Mean CP − Dearer CP) is always positive in magnitude.

Consistency of Units

While applying alligation, all values (Pulse 1, Pulse 2, and Mixture) must be in the same unit, i.e., all must be Cost Prices. If SP is given, convert it to CP first.

Shortcut Trick

Relative Speed = 100 + 60 = 160 km/h = 160 × (5/18) m/s.

Total distance (L + L/2) = 1.5L = Speed × Time = (160 × 5/18) × 27 = 1200 m.

Length of Train (L) = 1200 / 1.5 = 800 m.

Platform Crossing: (L + P) = Speed₁ × Time = (100 × 5/18) × 36 = 1000 m.

Length of Platform (P) = 1000 − 800 = 200 m.

∴ The correct answer is 200 m.

Alternate Method

Given: Speed₁ = 100 km/h, Speed₂ = 60 km/h, Time₁ = 27 s, Time₂ = 36 s.

Formula: Distance = Speed × Time; Relative Speed (Opposite) = S₁ + S₂.

⇒ Convert speeds: 100 km/h = 100 × (5/18) m/s; 60 km/h = 60 × (5/18) m/s.

⇒ Total Relative Speed = (100 + 60) × 5/18 = 160 × 5/18 = 400/9 m/s.

⇒ Total Distance = (L + L/2) = 1.5L = (400/9) × 27 = 1200 m.

⇒ L = 1200 / 1.5 = 800 m.

⇒ Distance during platform crossing = L + P = 100 × (5/18) × 36.

⇒ 800 + P = 100 × 5 × 2 = 1000 m.

⇒ P = 1000 − 800 = 200 m.

∴ The correct answer is 200 m.

Additional Information

Relative Speed

When moving in opposite directions, speeds are added (S₁ + S₂). When moving in the same direction, speeds are subtracted (S₁ − S₂).

Unit Conversion

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

Train-Platform Rule

When a train crosses a platform, bridge, or tunnel, total distance covered is Length of Train + Length of Object.

Shortcut Trick

Ratio of Profit = Σ(Investment × Time)

A: (400 × 10) + (700 × 2) = 4000 + 1400 = 5400

B: (600 × 5) + (700 × 7) = 3000 + 4900 = 7900

C: (800 × 7) = 5600

Profit Ratio A : B : C = 54 : 79 : 56. Total units = 189

Difference (C − A) = (56 − 54) = 2 units. Value = (2079 ÷ 189) × 2 = 11 × 2 = 22.

∴ The correct answer is Rs. 22.

Alternate Method

Given → Investment of A = Rs. 400, B = Rs. 600, C = Rs. 800. Time period = 12 months. Formulas: Profit Share = Investment × Time | Total Profit = Sum of individual shares.

⇒ Profit share of A = (400 × 10) + (400 + 300) × 2 = 4000 + 1400 = 5400. ⇒ Profit share of B = (600 × 5) + (600 + 100) × 7 = 3000 + 4900 = 7900. ⇒ Profit share of C = 800 × (12 − 5) = 800 × 7 = 5600. ⇒ Ratio A : B : C = 5400 : 7900 : 5600 = 54 : 79 : 56. ⇒ Sum of ratios = 54 + 79 + 56 = 189 units. ⇒ 189 units = Rs. 2079 ⇒ 1 unit = 2079 ÷ 189 = 11. ⇒ Difference (C − A) = 56 − 54 = 2 units. ⇒ Required difference = 2 × 11 = Rs. 22.

∴ The correct answer is Rs. 22.

Additional Information

Partnership Basics

When investments change over time, the profit is distributed based on the weighted average of investment with respect to time.

Profit Calculation

Profit of a partner = Investment × Duration. If multiple investments are made, Profit ∝ (I₁t₁ + I₂t₂ + ...).

Shortcut Trick

Total discount multiplier = (100 − 20)% × (100 − 10)% × (100 − 10)%

Selling Price = 2000 × 0.80 × 0.90 × 0.90

Selling Price = 2000 × 80/100 × 90/100 × 90/100

Selling Price = 2000 × 0.648 = 1296

∴ The correct answer is Rs. 1296.

Alternate Method

Given: Marked Price (MP) = Rs. 2000, Successive Discounts = 20%, 10%, and 10%. Formulas: Price after discount = MP × (100 − D₁)/100 × (100 − D₂)/100...

⇒ First discount = 20% of 2000 = 400. New price = 2000 − 400 = 1600. ⇒ Second discount = 10% of 1600 = 160. New price = 1600 − 160 = 1440. ⇒ Third discount = 10% of 1440 = 144. Final price = 1440 − 144 = 1296.

∴ The correct answer is Rs. 1296.

Additional Information

Successive Discounts

When a series of discounts are applied, each subsequent discount is calculated on the reduced price from the previous step. Formula for two discounts: a + b − (ab ÷ 100).

Marked Price vs Selling Price

Marked Price is the list price before any reductions. Selling Price is the actual amount paid by the customer after all discounts.

People: P, Q, R, S, T, U, V, and W.

Statements:

1. Q faces the center and sits third right of P. 
2. Only one person sits between Q and S, who is a neighbor of P.

Possibilities are:

3. Three people sit between V and S and V is facing the opposite direction of P. 

4. V is sitting second to the right of W.

5. S, W, and V are facing the same direction.

6. R is a neighbor of V and W. R is facing inside. 

7. Only one person sits between U and T. Both U and T facing the same direction. 

8. T is facing away from the center. Only one person sits between T and P, who is facing the opposite direction of T. 

According to statement 8 does not follow the possibility 2. So, we continue with possibility 1 only.

The final arrangement will be:

Hence, the answer is W.

People: P, Q, R, S, T, U, V, and W.

Statements:

1. Q faces the center and sits third right of P. 
2. Only one person sits between Q and S, who is a neighbor of P.

Possibilities are:

3. Three people sit between V and S, who are facing the opposite direction of P. 

4. V is sitting second to the right of W.

5. S, W, and V are facing the same direction.

6. R is a neighbor of V and W. R is facing inside.

7. Only one person sits between U and T. Both U and T facing the same direction. 

8. T is facing away from the center. Only one person sits between T and P, who is facing the opposite direction of T. 

According to statement 8 does not follow the possibility 2. So, we continue with possibility 1 only.

The final arrangement will be:

Hence, the answer is Q.

People: P, Q, R, S, T, U, V, and W.

Statements:

1. Q faces the center and sits third right of P. 
2. Only one person sits between Q and S, who is a neighbor of P.

Possibilities are:

3. Three people sit between V and S, who are facing the opposite direction of P. 

4. V is sitting second to the right of W.

5. S, W, and V are facing the same direction.

6. R is a neighbor of V and W. R is facing inside.

7. Only one person sits between U and T. Both U and T facing the same direction. 

8. T is facing away from the center. Only one person sits between T and P, who is facing the opposite direction of T. 

According to statement 8 does not follow the possibility 2. So, we continue with possibility 1 only.

The final arrangement will be:

Hence, the answer is immediately left.

People: P, Q, R, S, T, U, V, and W.

Statements:

1. Q faces the center and sits third right of P. 
2. Only one person sits between Q and S, who is a neighbor of P.

Possibilities are:

3. Three people sit between V and S, who are facing the opposite direction of P. 

4. V is sitting second to the right of W.

5. S, W, and V are facing the same direction.

6. R is a neighbor of V and W. R is facing inside.

7. Only one person sits between U and T. Both U and T facing the same direction. 

8. T is facing away from the center. Only one person sits between T and P, who is facing the opposite direction of T. 

According to statement 8 does not follow the possibility 2. So, we continue with possibility 1 only.

The final arrangement will be:

Hence, the answer is 5.

People: P, Q, R, S, T, U, V, and W.

Statements:

1. Q faces the center and sits third right of P. 
2. Only one person sits between Q and S, who is a neighbor of P.

Possibilities are:

3. Three people sit between V and S, who are facing the opposite direction of P. 

4. V is sitting second to the right of W.

5. S, W, and V are facing the same direction.

6. R is a neighbor of V and W. R is facing inside.

7. Only one person sits between U and T. Both U and T facing the same direction. 

8. T is facing away from the center. Only one person sits between T and P, who is facing the opposite direction of T. 

According to statement 8 does not follow the possibility 2. So, we continue with possibility 1 only.

The final arrangement will be:

Hence, the answer is T.

The best possible Venn diagram is,

Conclusions:

I. All Yellow being Blue is a possibility: True(as no such restriction is seen in the diagram above, it is possible)

II. Some Pink are Red: False (No direct relation between Red and Pink)

Hence, Only conclusion I follow.

Additional InformationOnly a few A are B means some A are B and some A are not B.

Some B is not A - false

All B being A is a possibility - true

All A being B is a possibility - false

The least possible diagram for the given statements is as follows;

Conclusions:

I. All Lakes can never be River → True (As Only a few Lakes are River so some lakes are river and some lakes are not river, as some lakes are not river all lakes can never be river is true) 

II. Some River can never be Salty → True (As Only a few River are Salty, some river are salty and some river are not salty, so some river can never be salty is true)

Hence, Both conclusions I and II follow.

The least possible diagram for the given statements is as follows;

Conclusions:

I. Some Masks are Belt → True (As All Belts are Masks → Some part of Masks will be Belts. So, it is true)

II. Some Mobile are Covers is a possibility → True (As there is no direct relation between Mobile and Covers but it is possible. So, it is true)

 Both conclusions I and II follow.

Six persons: P, Q, R, A, B, and C

Floors: 1, 2, and 3

Flat: X and Y

(1) P lives on an odd numbered floor in flat X. Therefore, we get two the following two cases here.

 

(2) The one who is from Finland lives immediately above C in the same flat.

(3) A lives to the west of C.

(4) P and the one who is from Finland do not live on the same floor.

 

(5) B does not live in flat Y.

(6) There is one floor between Q and the one who is from Serbia who lives above Q. Since, only flat Y of floor 3 is left for Q in case (I), case (I) eliminates here.

 

(7) Neither A nor Q is from Brazil.

(8) C is either from Mexico or from Nepal (implies, P is from Brazil).

(9) The one who is from Canada lives on the same floor on which the one who is from Nepal lives (implies, A is from Canada and C is from Nepal). Thus, the final arrangement is as follows:

 

As, we can see that all B, A, and P live in Flat X, whereas R lives in Flat Y.

Hence, R lives in Flat Y.