IBPS PO Prelims Memory Based Test (15th Oct 2022 Shift 2) (Previous Year Paper)

The correct answer is D.

Key Points

• The story of a bear is mentioned in the given passage.
• The first sentence is E. This sentence informs us about a bear who came across a log. Thus, the story begins.
• The second sentence is C. This sentence tells us that a little bee stung the bear on the nose when he went to inspect the log.
• The third sentence is B because it informs us that the bear became angry as the bee stung him.
• The fourth sentence is D because it informs us that the bees began to sting the bear as the bear was determined to destroy the nest of the bees.
• The last sentence is A. It concludes the passage by stating how the bear saved his life.
• The correct sequence is ECBDA.

Hint

• We use the article 'a' with a noun when we mention something about it for the first time. In E, the article 'a' is used before the word 'bear'. Thus, we can identify the first sentence.

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The following paragraph is formed after arranging the five sentences in proper sequence: 

A bear came across a log where a swarm of bees had nested to make their honey. As he came closer to inspect, a single little bee flew out of the log to protect the swarm and stung him sharply on the nose. This act by the little bee made the bear very angry and he was determined to destroy the nest of bees inside. This only alerted the bees and quick as a wink, the entire swarm of bees flew out of the log and began to sting the bear from head to heel. The bear saved himself from the bees by jumping into a nearby pond.

Additional Information

• Sting: to prick

The correct answer is C.

Key Points

• The story of a bear is mentioned in the given passage.
• The first sentence is E. This sentence informs us about a bear who came across a log. Thus, the story begins.
• The second sentence is C. This sentence tells us that a little bee stung the bear on the nose when he went to inspect the log.
• The third sentence is B because it informs us that the bear became angry as the bee stung him.
• The fourth sentence is D because it informs us that the bees began to sting the bear as the bear was determined to destroy the nest of the bees.
• The last sentence is A. It concludes the passage by stating how the bear saved his life.
• The correct sequence is ECBDA.

Hint

• We use the article 'a' with a noun when we mention something about it for the first time. In E, the article 'a' is used before the word 'bear'. Thus, we can identify the first sentence.

<br>

The following paragraph is formed after arranging the five sentences in proper sequence: 

A bear came across a log where a swarm of bees had nested to make their honey. As he came closer to inspect, a single little bee flew out of the log to protect the swarm and stung him sharply on the nose. This act by the little bee made the bear very angry and he was determined to destroy the nest of bees inside. This only alerted the bees and quick as a wink, the entire swarm of bees flew out of the log and began to sting the bear from head to heel. The bear saved himself from the bees by jumping into a nearby pond.

Additional Information

• Swarm: a large number of flying insects

The correct answer is E.

Key Points

• The story of a bear is mentioned in the given passage.
• The first sentence is E. This sentence informs us about a bear who came across a log. Thus, the story begins.
• The second sentence is C. This sentence tells us that a little bee stung the bear on the nose when he went to inspect the log.
• The third sentence is B because it informs us that the bear became angry as the bee stung him.
• The fourth sentence is D because it informs us that the bees began to sting the bear as the bear was determined to destroy the nest of the bees.
• The last sentence is A. It concludes the passage by stating how the bear saved his life.
• The correct sequence is ECBDA.

Hint

• We use the article 'a' with a noun when we mention something about it for the first time. In E, the article 'a' is used before the word 'bear'. Thus, we can identify the first sentence.

<br>

The following paragraph is formed after arranging the five sentences in proper sequence: 

A bear came across a log where a swarm of bees had nested to make their honey. As he came closer to inspect, a single little bee flew out of the log to protect the swarm and stung him sharply on the nose. This act by the little bee made the bear very angry and he was determined to destroy the nest of bees inside. This only alerted the bees and quick as a wink, the entire swarm of bees flew out of the log and began to sting the bear from head to heel. The bear saved himself from the bees by jumping into a nearby pond.

Additional Information

• Inspect: examine or check

The correct answer is B.

Key Points

• The story of a bear is mentioned in the given passage.
• The first sentence is E. This sentence informs us about a bear who came across a log. Thus, the story begins.
• The second sentence is C. This sentence tells us that a little bee stung the bear on the nose when he went to inspect the log.
• The third sentence is B because it informs us that the bear became angry as the bee stung him.
• The fourth sentence is D because it informs us that the bees began to sting the bear as the bear was determined to destroy the nest of the bees.
• The last sentence is A. It concludes the passage by stating how the bear saved his life.
• The correct sequence is ECBDA.

Hint

• We use the article 'a' with a noun when we mention something about it for the first time. In E, the article 'a' is used before the word 'bear'. Thus, we can identify the first sentence.

<br>

The following paragraph is formed after arranging the five sentences in proper sequence: 

A bear came across a log where a swarm of bees had nested to make their honey. As he came closer to inspect, a single little bee flew out of the log to protect the swarm and stung him sharply on the nose. This act by the little bee made the bear very angry and he was determined to destroy the nest of bees inside. This only alerted the bees and quick as a wink, the entire swarm of bees flew out of the log and began to sting the bear from head to heel. The bear saved himself from the bees by jumping into a nearby pond.

<br>

Additional Information

• Determined: to decide firmly

The correct answer is A.

Key Points

• The story of a bear is mentioned in the given passage.
• The first sentence is E. This sentence informs us about a bear who came across a log. Thus, the story begins.
• The second sentence is C. This sentence tells us that a little bee stung the bear on the nose when he went to inspect the log.
• The third sentence is B because it informs us that the bear became angry as the bee stung him.
• The fourth sentence is D because it informs us that the bees began to sting the bear as the bear was determined to destroy the nest of the bees.
• The last sentence is A. It concludes the passage by stating how the bear saved his life.
• The correct sequence is ECBDA.

Hint 

• We use the article 'a' with a noun when we mention something about it for the first time. In E, the article 'a' is used before the word 'bear'. Thus, we can identify the first sentence.

<br>

The following paragraph is formed after arranging the five sentences in proper sequence: 

A bear came across a log where a swarm of bees had nested to make their honey. As he came closer to inspect, a single little bee flew out of the log to protect the swarm and stung him sharply on the nose. This act by the little bee made the bear very angry and he was determined to destroy the nest of bees inside. This only alerted the bees and quick as a wink, the entire swarm of bees flew out of the log and began to sting the bear from head to heel. The bear saved himself from the bees by jumping into a nearby pond.

The correct answer is option 2, i.e. 'C-E and B-D'.

Key Points

• The sentences formed after joining the phrases C and E, and B and D respectively are:
• C-E: 'A wave of grief swept through the country when the PM was assassinated​',
• B-D: 'Students across the country rejoiced when the new education policy was rolled out'.
• Both these sentences are grammatically and contextually correct.
• All other options are incorrect as the sentences formed are either grammatically or contextually incorrect.

The correct answer is option 1, i.e., 'B-F and A-E'.

Key Points

• The sentences formed after joining the phrases B and F, and A and E respectively are: 
• 'When will it dawn on the government that there is raging discontent in rural areas?'
• 'When was the last time that you paid a visit to your family?'.
• Both these sentences are grammatically and contextually correct.
• All other options are incorrect as the sentences formed are either grammatically or contextually incorrect.

Key PointsLet's join the sentences to give a contextually and grammatically meaningful sentence. 

The correct sequences are:

A talks about 'regional parties', which is connected to 'regional issues' in E. So, A-E

B talks about 'being no case for' something, which is related to 'for hastening the intoduction' in D. So, B-D

C talks about 'according something', which is related to 'priority' in F. So, C-F

Out of these, only C-F and B-D is expressed in the given options.

Therefore, the correct answer is option 4.

The only correct sentence is 'He was dressed in black, and had a very pleasant face.'

Key Points

• Option 1- "He was dressed in black, and had a very pleasant face."
• The sentence is in the past tense. 'He was dressed' is correctly written as the word 'was' is written in the past tense. 'had a very pleasant face' is also written correctly as 'had' shows past tense action. The preposition 'in' and the adverb 'very' are also placed correctly and appropriately.
• Option 2- "He, therefore, put the finances in the best order he could, and set himself to mitigate the evil effects to the war by obtaining an early peace."
• The error lies in the preposition 'to'. It is incorrect. 'To' will be replaced with 'of'.
• The correct sentence is- "He, therefore, put the finances in the best order he could, and set himself to mitigate the evil effects of the war by obtaining an early peace."
• Option 3- " I've have a miserable cold for the past week."
• The repetition of 'have' is incorrect.
• The correct form of the verb will be 'had'. Therefore, the correct sentence- "I've had a miserable cold for the past week."
• Option 4- "They're afraid which we might aggravate an already bad situation."
• The usage of the pronoun 'which' is incorrect. It should be replaced with 'that'.
• The correct sentence is- "They're afraid that we might aggravate an already bad situation."
• Hence, the correct answer is option 1.

The correct answer is 'All are correct'.

Key Points

• Option 1- "My bike that has a broken seat is in the garage."
• The usage of 'has' is correct, it indicates that the speaker's bike possesses a broken seat.
• 'That' the usage of pronoun is absolutely correct.
• The usage of article 'a' is used correctly.
• The verb 'is' is correctly used, indicating present tense.
• The preposition 'in' is also correct.
• Option 2- "Older people who are unfamiliar with computer technology often have an aversion to it."
• Older is the comparative form of old and is an adjective defining a particular type of people.
• 'Who' pronoun is correctly used referring to 'older people'.
• The prepositions 'with' and 'to' are also correctly used.
• Option 3- "Pierre turned away with repugnance, and closing his eyes quickly fell back on the carriage seat."
• Turned away means to refuse admittance or acceptance.
• Repugnance means- intense disgust.
• 'His' pronoun is correctly used referring to 'Pierre'. The adverb 'Quickly' is used correctly defining how he fell back on the carriage seat.
• Option 4- "I like that sweater; however, it only comes in one color."
• This sentence is correct. 'That' pronoun is used correctly.
• The conjunction 'however' is correctly used.
• 'Only' is used as an adverb here and is correctly used.
• Hence, the correct answer is option 5.

The correct answer is An erratic monsoon season can damage the economy and affect agricultural practices.

Key Points

• The sentence 'An erratic monsoon season can damage the economy and affect agricultural practices.' is grammatically correct.
• The article 'an' is used before the word 'erratic' because it begins with a vowel sound.
• The base form of the verb 'damage' and 'affect' is used after the modal verb 'can'.
• The conjunction 'and' is also appropriate.
• Hence, the sentence is grammatically correct.
• The corrected form of the other sentences are:
• | Option | Grammatical mistake | Corrected sentence | | --- | --- | --- | | 1. | The conjunction 'so' should be replaced with 'and' | Around 64 per cent of land used for agriculture and food crops is at risk of pesticide pollution. | | 3. | The base form of the verb 'increased', i.e. 'increase' should be used here. | The intensity of cyclones and hurricanes might increase in the next century due to global warming. | | 4. | The word 'develop' should be replaced with the word 'develops'. | Robotics develops machines that can substitute for humans and replicate human actions. |

 

• Therefore, option 2) is the answer.

Additional Information

• Erratic: unpredictable or inconstant

The correct answer is 'Jaipur.'

Key Points

• The first sentence of the first paragraph says "AU Small Finance Bank Limited is an Indian Small finance bank, based in Jaipur, India.''
• From the above sentence, we can say that the headquarters of AU Small Finance Bank is in Jaipur.
  

Hence, the only possible answer is option 2.

The correct answer is 'Sanjay Agarwal.'

Key Points

• The first sentence of the second paragraph says "The company was founded by Sanjay Agarwal (managing director and CEO of AU Small Finance Bank) as a private limited company, and publicly listed in an IPO on 29 June 2017.''
• From the above sentence, we can say that Sanjay Agarwal is the founder of AU Small Finance Bank.
  

Hence, the only possible answer is option 1.

The correct answer is '28.5% stake.'

Key Points

• The second sentence of the second paragraph says "A merit holder Chartered Accountant and a first-generation entrepreneur, he holds ~28.5% stake in the Bank.''
• From the above sentence, we can say that the founder of AU Small Finance Bank has approx 28.5% stake in AU Small Finance Bank.
  

Hence, the only possible answer is option 2.

The correct answer is 'Ameliorating.'

Key Points

• The word 'Improving' means To make or become better.
• Example: Management needs to explore ways of improving office security.
• Let's look at the meaning of the given options:-
• Impairing - To weaken or damage.
• Example: Many governments could increase their tax receipts without impairing the efficiency of their economies.
• Tarnishing - To make or become less valuable or respected.
• Example: It is not the opposition that is tarnishing the image of the regime.
• Vitiating - To make something less effective; to spoil something.
• Example: *The insurance company is *vitiating.
• Ameliorating - To make something better.
• Example: Government has assumed the responsibility for ameliorating income inequality in our society.
• Deteriorating - To become progressively worse.
• Example: Standards of living were deteriorating rather noticeably.
  

Hence, the only possible answer is option 4.

Additional Information

• The synonyms of the word 'Improving' are "Ameliorating, Enhancing, Boosting".
• The antonyms of the word 'Improving' are "Impairing, Deteriorating, Tarnishing".

The correct answer is 'Economical.'

Key Points

• The word 'Expensive' means Costing a lot of money.
• Example: She was wearing an expensive new outfit.
• Let's look at the meaning of the given options:-
• Economical - Cheap; inexpensive.
• Example: My new car is economical in fuel.
• Extortionate - Much too high; exorbitant.
• Example: The price of books nowadays is extortionate.
• Extravagant - Exceeding what is reasonable or appropriate; excessive or elaborate.
• Example: He had a wildly extravagant lifestyle.
• Valuable - Worth a great deal of money.
• Example: He spent hours bargaining for the valuable watch.
• Exorbitant - Unreasonably high; expensive.
• Example: The price of food here is exorbitant.
  

Hence, the only possible answer is option 1.

Additional Information

• The antonyms of the word 'Expensive' are "Economical, Cheap, Inexpensive".
• The synonyms of the word 'Expensive' are "Extortionate, Extravagant, Exorbitant".

The correct answer is 'Commencing on or from a certain time or date.'

Key Points

• Given Idiom: As of means Commencing on or from a certain time or date.
• Example: As of last December our meetings have been open to the public.
• From the given options, the third option is the most appropriate meaning of the given idiom*.*
  

Hence, the correct answer is option 3.

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Mistake Points

• We may think from the phrase "As of" that it is all about something close to the actual, but not completely accurate or exact.
  

Additional Information

• This idiom was first used in business but came into more general use in c.1900*.*

The correct answer is 'Comprises.'

Key Points

• The given sentence is saying that AU Small Finance Bank's distribution network consists of 758 Banking Touchpoints and 23,486 employees.
• Therefore, the most appropriate word to be filled in the blank is 'Comprises'.
• Also, the use of the word ''across'' in the sentence indicates the use of the word 'comprises' in the blank.
• The word 'Comprises' means Consist of; be made up of.
• Example: The committee comprises men of widely different views.
  

Hence, the correct answer is option 3.

Complete Sentence: As on June 30, 2021, AU Small Finance Bank's distribution network comprises 758 Banking Touchpoints, and 23,486 employees spread contiguously across 15 states and two Union Territories with over 2 million customers.

Additional Information

• Let us explore  the other options:
• Considerate means Careful not to inconvenience or harm others.
• Wary means Feeling or showing caution about possible dangers or problems.
• Imprudent means Not showing care for the consequences of an action; rash.
• Compromises means To settle a dispute by mutual concession.

The correct answer is 'Vehicle finance company.'

Key Points

• The second sentence of the first paragraph says "It was founded as vehicle finance company AU Financiers (India) Ltd in 1996 and converted to a small finance bank on 19 April 2017.''
• From the above sentence, we can say that according to the passage, AU Small Finance Bank Limited was founded as a vehicle finance company.
  

Hence, the only possible answer is option 3.

The correct answer is researched.

Key Points

The explanation is as follows:

• The given statement shows completed action.
• The simple past is used for a completed action.
• It often is used with signal words or phrases such as "yesterday," "last week," "1 year ago," or "in 2015", etc.
• It is used to indicate the specific time in the past when the action took place.
• Example: Aparna went to China in 2010.
• The word researched is in the simple past form.

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Hence, the correct sentence is In the past, Zimbardo researched many aspects of social psychology.

Additional Information

Simple Past:

• It is verb tense.
• It is used to talk about things that happened or existed before now.
• Examples:
• She saw a movie yesterday.
• She didn't see the work yesterday.
• Last year, she traveled to Japan.
• Last year, she didn't travel to Korea.
• Did you have dinner last night?
• She washed her car.

The correct answer is 'sitting'.

Key Points

• There are some verbs followed by gerunds. i.e. prefer, advise, allow, can't help, deny, detest, dislike, love etc.
• Here in the sentence, the verb 'prefers' should also be followed by gerunds( sit+ing)
• Hence, Option 2 is the correct answer.
  

The correct sentence is: He prefers sitting at the back of the movie theatre.

Additional Information 

What are Gerunds?

• A gerund is a verb in its ing (present participle) form that functions as a noun that names an activity rather than a person or thing. Any action verb can be made into a gerund.
• Gerunds can appear at the beginning of a sentence when used as a subject:
• Ex: Jogging is a hobby of mine.
• Gerunds can act as an object following the verb:
• Ex: Daniel quit smoking a year ago.
• Gerunds can serve as an object after a preposition:
• Ex: I look forward to helping you paint the house.

The correct solution is option 4 i.e. ‘bring’.

• The sentence is in the past tense as ‘did’ is used.
• Also, whenever ‘did’ is used, the verb that follows it must be in its base form.
• So, we have to use 'bring' in the blank.
• Other options are rejected because :
• ‘Bringing’ is the gerund and the present participle of 'bring'.
• 'Was bringing’ is wrong because it is in the past continuous tense.
• ‘Had bought’ is in the past perfect tense which indicates that an action was completed at some point in the past before something else happened.
• 'Bought' is the past tense and past participle of 'buy'.

The correct answer is 'B'.

Key Points

• The correct spelling is  'Mercurial'.
• Let's explore the meaning and context of it.
• Mercurial:  changing suddenly and without warning; reacting in an unexpected way
  

Ex: She was entertaining but unpredictable, with mercurial mood swings.

• Thus the correct answer is Option 2.

Additional Information Let's explore the meaning of other options as well.

• Quicksilver: the liquid metal mercury.
• Behaviour: Her behaviour is often appalling.
• Unreliable: not able to be relied upon.

The correct answer is 'B'.

Key Points

• The correct spelling is 'Deprecate'.
• Let's explore the meaning and context of it.
• Deprecate: Express strong disapproval of; deplore (कड़ी अस्वीकृति व्यक्त करें)
• Ex: The teacher should not deprecate his student's efforts.
• Thus the correct answer is Option 2.

Additional Information

• Let's explore the meaning of other options as well.
• Courtesy: A courteous, respectful or considerate act (एक विनम्र, सम्मानजनक या विचारशील कार्य)
• Tendency: An inclination to do something (कुछ करने का जज्बा)
• Acquaintances: A relationship less intimate than friendship (दोस्ती से कम घनिष्ठ रिश्ता)

The correct answer is 'D'.

Key Points

• The correct spelling is 'Etiquette'.
• Let's explore the meaning and context of it.
• Etiquette: The set of rules or customs that control accepted behaviour 
  

Ex: Social etiquette dictates that men cannot sit while women are standing.

• Thus the correct answer is Option 4.

Additional Information Let's explore the meaning of other options as well.

• Refusal: saying or showing that you will not do, give or accept something
• Particularly: used to emphasize that you are talking about one person, thing, time, etc. and not about others
• Breach: an act of breaking a law, promise, agreement, or relationship.

The correct answer is 'A'.

Key Points

• The correct spelling is  'Embarrassed'.
• Let's explore the meaning and context of it.
• Embarrassed: feeling ashamed or shy.
  

Ex: She felt embarrassed about undressing in front of the doctor.

• Thus the correct answer is Option 1.

Additional Information Let's explore the meaning of other options as well.

• Discipline: the ability to control yourself or other people, even in difficult situations.
• Hypothetical: imagined or suggested but not necessarily real or true.
• Article: a piece of writing on a particular subject in a newspaper or magazine.

The correct answer is Both 1 and 2.

 

Key Points

Both Despite and In spite of are negative conjunctions.

• Despite/ In spite of: without being affected by.
• In spite agrees with the preposition "of".
• Despite is used independently.
• Therefore, the correct answer is: Despite/ In spite of working hard, Barcelona couldn't make it to the semi-final of the Champions League.

The correct answer is going to have

Key Points

• The sentence is talking about an incident that may happen in the future.
• The sentence also uses a conditional phrase.
• The party will only take place given the person scores well.
• 'Have' should be used instead of 'has' as the first-person subject always takes the plural 'have'.
• Thus, 'going to have' should be used.

​

Important Points 

• Going to is not a tense.
• It is a special structure that we use to talk about the future.

The structure of going to is:

• subject + be + going + to infinitive
• Example: I am going to go to a movie tomorrow.

The correct answer is CDEAB.

Key Points

• C is the part that establishes the beginning of the matter,i.e., ' A 500-year-old ancient  '. Hence, it will be the first part after rearrangement.
• Part D refers to the drain in Scotland. Hence, D follows C.
• Now part E states that this drain lay undisturbed for a long time. So, part E follows D.
• Part A talks about the time it was discovered and how it is turning to be a goldmine, so it must come after part E.
• Part B talks about the importance of the Scotland drain for archaeologists from Glasgow University. Hence, B follows A.

​

Correct rearrangement of segments is - A 500-year-old ancient drain in Scotland, which ay undisturbed until its discovery in 1990, is turning out to be a goldmine for the archaeologists from the Glasgow University.

Hint

• While solving jumbles, one must first look for any independent sentences/segments or the option which establishes the subject matter.
• Then, one must look for connections between the sentences/segments.
• Some sentences/segments might have some concluding notion. So these parts will always be at the end.

​

The correct answer is ECABD.

Key Points

• E is the part that establishes the subject of the matter,i.e., 'many electronic firms '. Hence, it will be the first part after rearrangement.
• Part C refers to what these firms have created. Hence, D follows B.
• Now three parts are remaining, and out of them, part A talks about development departments being created. So, part A follows C.
• Part B talks about qualities like highly qualified and well paid, so it must come after part A.
• Part D talks about scientists and technicians  Hence, D follows B.

​

Correct rearrangement of segments is - Many electronic firms had recently created research and development departments employing highly qualified and well-paid scientists and technicians.

Hint

• While solving jumbles, one must first look for any independent sentences/segments or the option which establishes the subject matter.
• Then, one must look for connections between the sentences/segments.
• Some sentences/segments might have some concluding notion. So these parts will always be at the end.

​

 

Steel bottle is manufactured by A is 122 and copper bottle is =122+21 = 143

Copper A and Steel B is in ratio 13: 17 

⇒ 13 unit = 143 then 17 is equal to 187

Copper bottle by B is 25 more than the copper by A = 143+25 = 168

Copper bottle manufactured by C is 164 then Steel bottle is 216

Then average no of steels bottles manufactured by all 

⇒ 122+187+216 = 525

⇒ 525/3

⇒ 175

Hence 175 is the correct answer.

Total no of copper bottles in shop C is 164

Total no of steel bottles in all three shops is 525 

⇒( 164 / 525 ) ×100

⇒ 31.23% ~ 32%

Hence 32% is the correct answer.

Steel bottles in shop C is 216

Shop D of copper bottles  is 25% more than steel shop C

⇒ 216 × 125 / 100

⇒ 216× 5 /4

⇒ 270 unit 

Copper bottles in shop A is 143 

Then Ratio of these respective entities is 143 : 270

Hence 143 : 270 is the right answer.

Total no of steel bottles in all three shops is 525 units 

Total no of copper bottles in all three shops is 475 units 

Required difference is ,

⇒ 525 - 475 

⇒ 50 units 

Hence 50 is the correct answer.

Cost price of  copper bottles is Rs 250

Cost price of silver bottles is Rs 300

Profit earned by Shop selling all bottles 

⇒ 187× 300 + 250 × 168

⇒ 56100 + 42000

⇒ Rs 98100

Hence Rs 98100 is the correct answer.

Shortcut Trick

Ratio change in P and Q from 3:4 to 6:7 involves an increase of 3 units each (6−3 = 3 and 7−4 = 3).

This 3 units increase corresponds to 27 years.

∴ 1 unit = 27 ÷ 3 = 9 years.

Present age of Q = 4 units = 4 × 9 = 36 years.

∴ The correct answer is 36 years.

Alternate Method

Given:

Ratio of present ages of P and Q = 3:4

Difference between P and Q = 9 years

Calculations:

Let the present age of P be 3x and Q be 4x.

⇒ 4x − 3x = 9

⇒ x = 9

⇒ Present age of Q = 4x

⇒ 4 × 9 = 36 years

Verification with future ratio:

⇒ (27 + 27) / (36 + 27) = 54 / 63 = 6 / 7 (Correct)

∴ The correct answer is 36 years.

Additional Information

Age Difference Property

The difference between the ages of two persons remains constant at any point in time (past, present, or future).

Ratio Balancing Method

If the difference in ratio parts between two periods is not the same, multiply the ratios by the difference of the other ratio to balance the gaps.

Shortcut Trick

Let Efficiency of P = 2 units/day → Q = 3 units/day (50% more).

Total Work = 30 days × 2 = 60 units.

Days taken by Q = 60 ÷ 3 = 20 days. Days for R = 20 − 10 = 10 days.

Efficiency of R = 60 ÷ 10 = 6 units/day.

Equation: (Efficiency_R+Q × X) + (Efficiency_P × (X + 8)) = 60

⇒ (6 + 3)X + 2(X + 8) = 60 ⇒ 9X + 2X + 16 = 60 ⇒ 11X = 44 ⇒ X = 4.

∴ The correct answer is 4.

Alternate Method

Given: P completes task in 30 days. Q is 50% more efficient than P. R takes 10 days less than Q.

Calculations:

⇒ Efficiency of Q = 1.5 × Efficiency of P. If P = 2, then Q = 3.

⇒ Total Work = Days × Efficiency = 30 × 2 = 60 units.

⇒ Days taken by Q = 60 ÷ 3 = 20 days.

⇒ Days taken by R = 20 − 10 = 10 days.

⇒ Efficiency of R = 60 ÷ 10 = 6 units/day.

⇒ Combined efficiency of R and Q = 6 + 3 = 9 units/day.

⇒ Work done by R and Q in X days = 9X.

⇒ Work done by P in (X + 8) days = 2(X + 8).

⇒ 9X + 2(X + 8) = 60

⇒ 9X + 2X + 16 = 60

⇒ 11X = 44

⇒ X = 4.

∴ The correct answer is 4.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a work. If the ratio of efficiency is a:b, the ratio of time taken is b:a.

Work and Wages

Wages are generally distributed in the ratio of the work done by each individual, which is (Efficiency × Time).

Combined Work Formula

If A and B work together, their combined efficiency is the sum of their individual efficiencies. Total Work = (E_A + E_B) × Time.

Shortcut Trick

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

Given Difference (D) = ₹15 and Rate (r) = 5%.

15 = P × (5/100) × (5/100)

15 = P × (1/20) × (1/20) ⇒ 15 = P ÷ 400

P = 15 × 400 = ₹6,000.

∴ The correct answer is ₹6,000.

Alternate Method

Given: Difference (D) = ₹15, Time (T) = 2 years, Rate (R) = 5%

Formula Used: D = P(R/100)²

⇒ 15 = P × (5/100)²

⇒ 15 = P × (25/10000)

⇒ 15 = P × (1/400)

⇒ P = 15 × 400

⇒ P = 6,000

∴ The correct answer is ₹6,000.

Additional Information

CI vs SI Difference for 3 Years

The formula for the difference for 3 years is D = P(r/100)² × (300 + r)/100.

Effective Rate Method

For 2 years, SI effective rate = 2r%. CI effective rate = (2r + r²/100)%. Difference = (r²/100)% of Principal.

Compound Interest Formula

Amount (A) = P(1 + r/100)ⁿ, where n is the number of years and r is the annual interest rate.

Shortcut Trick

Initial Ratio of Water : Alcohol = 2 : 1. After removing 12 liters, the ratio remains 2 : 1.

Let quantities be 2x and 1x. Replacing 12 liters of mixture with 12 liters of water gives:

(2x + 12) / 1x = 4 / 1 ⇒ 2x + 12 = 4x ⇒ 2x = 12 ⇒ x = 6 liters.

Quantity of Alcohol after removal = 6 liters. Initial Alcohol = 6 + (1/3 × 12) = 10 liters.

∴ The correct answer is 10 litres.

Alternate Method

Given: Initial ratio Water : Alcohol = 2 : 1. Final ratio after replacing 12L mixture with 12L water = 4 : 1.

Let the initial total mixture be T liters.

⇒ Initial Water = 2T/3, Initial Alcohol = T/3.

⇒ Alcohol removed in 12L = (1/3) × 12 = 4 liters.

⇒ Water removed in 12L = (2/3) × 12 = 8 liters.

⇒ New Alcohol = (T/3) − 4.

⇒ New Water = (2T/3) − 8 + 12 = (2T/3) + 4.

⇒ Final Ratio: ((2T/3) + 4) / ((T/3) − 4) = 4 / 1.

⇒ (2T/3) + 4 = 4 × ((T/3) − 4) ⇒ 2T/3 + 4 = 4T/3 − 16.

⇒ 2T/3 = 20 ⇒ T = 30 liters.

⇒ Initial Alcohol = T/3 = 30 / 3 = 10 liters.

∴ The correct answer is 10 litres.

Additional Information

Ratio in Mixtures

When a portion of a mixture is removed, the ratio of components in the remaining mixture stays the same as the initial ratio.

Replacement Rule

Final Quantity = Initial Quantity × (1 − Replacement Volume / Total Volume)ⁿ. This applies when the same component is repeatedly replaced.

Shortcut Trick

Investment ratio = (Profit ratio ÷ Time period ratio).

Time periods: A = 12 months, B = 9 months, C = 6 months. Ratio = 4 : 3 : 2.

Profit ratio = 2 : 3 : 5.

Investment ratio = (2/4) : (3/3) : (5/2) = 0.5 : 1 : 2.5 = 1 : 2 : 5.

Given A's investment (1 unit) = Rs. 36000.

Difference between B and C = 5 − 2 = 3 units = 3 × 36000 = Rs. 108000.

∴ The correct answer is Rs. 108000.

Alternate Method

Given: A's investment = Rs. 36000. Time of A = 12 months, B = 9 months, C = 6 months. Profit ratio A : B : C = 2 : 3 : 5.

Formulas: Profit = Investment × Time | Investment = Profit ÷ Time

⇒ Let B's investment be I_B and C's investment be I_C.

⇒ Ratio of profits = (36000 × 12) : (I_B × 9) : (I_C × 6) = 2 : 3 : 5

⇒ For A and B: (36000 × 12) / (I_B × 9) = 2 / 3

⇒ (4000 × 12) / I_B = 2 / 3 ⇒ 48000 / I_B = 2 / 3 ⇒ I_B = (48000 × 3) / 2 = Rs. 72000

⇒ For A and C: (36000 × 12) / (I_C × 6) = 2 / 5

⇒ (6000 × 12) / I_C = 2 / 5 ⇒ 72000 / I_C = 2 / 5 ⇒ I_C = (72000 × 5) / 2 = Rs. 180000

⇒ Difference = I_C − I_B = 180000 − 72000 = Rs. 108000

∴ The correct answer is Rs. 108000.

Additional Information

Partnership Basics

In a partnership, the profit is shared in the ratio of the product of Capital (Investment) and Time. If time is constant, profit ratio is the same as investment ratio.

Ratio of Investments

If profits P₁, P₂ are earned in times T₁, T₂, then the ratio of investments I₁ : I₂ = (P₁/T₁) : (P₂/T₂).

Shortcut Trick

Let Length of Train B = L, then Length of Train A = L/2.

Let Speed of Train A = 2x and Speed of Train B = 3x.

Using Distance = Speed × Time: (L/2 + 100) / 5 = 2x and (L + 100) / 6 = 3x.

Ratio of speeds: [(L + 200)/10] / [(L + 100)/6] = 2/3 ⇒ 3(L + 200)/10 = 2(L + 100)/6.

Solving for L: 9L + 1800 = 10L + 1000 ⇒ L = 800 m.

∴ The correct answer is 800 m.

Alternate Method

Given: Ratio of lengths A:B = 1:2. Ratio of speeds A:B = 2:3. Platform = 100 m.

Formula Used: Speed = (Length of Train + Length of Platform) ÷ Time

⇒ Speed of A = (L_A + 100) ÷ 5

⇒ Speed of B = (L_B + 100) ÷ 6

⇒ Let L_B = 2y, then L_A = y

⇒ [(y + 100) ÷ 5] / [(2y + 100) ÷ 6] = 2 ÷ 3

⇒ [6(y + 100)] / [5(2y + 100)] = 2 / 3

⇒ 18(y + 100) = 10(2y + 100)

⇒ 18y + 1800 = 20y + 1000

⇒ 2y = 800

⇒ L_B = 2y = 800 m

∴ The correct answer is 800 m.

Additional Information

Train Crossing Object with Length

When a train crosses a platform, bridge, or another train, the total distance covered is the sum of the train's length and the object's length.

Relative Speed

If two trains are moving in the same direction, relative speed = S₁ − S₂. In opposite directions, relative speed = S₁ + S₂.

Conversion Units

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

I. x² + 13x + 42 = 0 

⇒ x² + 7x + 6x + 42 = 0 

⇒ (x + 6)(x + 7) = 0

⇒ x = -6, -7

II. y² – 2y - 63 = 0 

⇒ y² – 9y + 7y - 63 = 0 

⇒ (y – 9)(y + 7) = 0

⇒ y = 9, -7

 

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

Given: 

I. x2 - 2x - 8 = 0

II. y2  - 7y - 60 = 0

Concept used:

Using quadratic equation.

Calculation:

From I,

x2 - 2x - 8 = 0

⇒ x² - 4x + 2x - 8 = 0

⇒ x(x - 4) + 2(x - 4) = 0

⇒ (x - 4) (x + 2) = 0

⇒ x = 4, - 2

From II,

y2  - 7y - 60 = 0

⇒ y² - 12y + 5y - 60 = 0

⇒ y(y - 12) + 5(y - 12) = 0

⇒ (y - 12) (y + 5) = 0

⇒ y = 12, -5

Comparison between x and y (via Tabulation):

 

∴ The relationship between x and y cannot be established.

Given:

I) 9x2 - 3x - 2 = 0

II) y2 - 8y + 16 = 0

Concept used:

Using quadratic equation

Calculation:

From I,

9x2 - 3x - 2 = 0

⇒ 9x²  - 6x + 3x - 2 = 0

⇒ 3x(3x - 2) + 1(3x - 2) = 0

⇒ (3x - 2) (3x + 1) = 0

⇒ x = 2/3, - 1/3

From II,

y2 - 8y + 16 = 0

⇒ y² - 4y - 4y + 16 = 0

⇒ y(y - 4) - 4(y - 4) = 0

⇒ (y - 4) (y - 4) = 0

⇒ y = 4, 4

Comparison between x and y (via Tabulation):

 

∴ x < y.

Calculation:

I. x² – 12x + 32 = 0

⇒ x² – 8x – 4x + 32 = 0

⇒ x(x – 8) – 4(x – 8) = 0

⇒ (x – 4)(x – 8) = 0

⇒ x = 4, 8

II.  2y² – 9y + 10 = 0

⇒ 2y² – 4y – 5y + 10 = 0

⇒ 2y(y – 2) – 5(y – 2) = 0

⇒ (2y – 5)(y – 2) = 0

⇒ y = 5/2, 2

 

∴ The relation between x and y is x > y

Calculation∶

I. x² - 15x + 54 = 0

⇒ x² - 6x - 9x + 54 = 0

⇒ x(x - 6) - 9(x - 6) = 0

⇒ (x - 6)(x - 9) = 0

⇒ x = 6, 9

II. y² - 11y + 24 = 0

⇒ y² - 3y - 8y + 24 = 0

⇒ y(y - 3) - 8(y - 3) = 0

⇒ (y - 3)(y - 8) = 0

⇒ y = 3, 8

 

∴ Relationship between x and y cannot be established

Calculation:

Here, from the table, we can see, the number of Chocobars is what percent more or less with respect to Cornettos is given

So, we can say, Arun has 20% more Chocobars than Cornettos 

Let, the total number of Cornettos be 100

So, the ratio of Chocobars and Cornettos = (100 + 20) ∶ 100

⇒ 6 ∶ 5

Similarly, we can say the same for others,

So, put those data in a table, we get,

 

The number of Chocober ice creams Sonal had = 160

The number of Cornetto ice creams she had = 100

So, the required percentage = {(160/100) × 100} = 160%

∴ The number of Chocobar ice creams that Sonal had been 160% of the number of Cornetto ice creams she had.

Alternate Method

Concept used:

Here, we can use the ratio of two ice creams and get the desired result

Calculation:

So, the required percentage = (8/5) × 100 = 160%

∴ The number of Chocobar ice creams that Sonal had been 160% of the number of Cornetto ice creams she had.

Calculation:

Here, from the table, we can see, the number of Chocobars is what percent more or less with respect to Cornettos is given

So, we can say, Arun has 20% more Chocobars than Cornettos 

Let, the total number of Cornettos be 100

So, the ratio of Chocobars and Cornettos = (100 + 20) ∶ 100

⇒ 6 ∶ 5

Similarly, we can say the same for others,

So, put those data on a table, we get,

 

The total number of Cornettos Arun and Kiran has = (100 + 200) = 300

T he total number of Chocobars Barun and Rumi has = (140 + 100) = 240

So, the difference = (300 - 240) = 60

∴ The required difference is 60.

Calculation:

Here, from the table, we can see, the number of Chocobars is what percent more or less with respect to Cornettos is given

So, we can say, Arun has 20% more Chocobars than Cornettos 

Let, the total number of Cornettos be 100

So, the ratio of Chocobars and Cornettos = (100 + 20) ∶ 100

⇒ 6 ∶ 5

Similarly, we can say the same for others,

So, put those data in a table, we get,

 

As per the table, we get

The total number of Chocobar ice creams = (120 + 140 + 180 + 100 + 160) = 700

So, the average number of Chocobar ice creams they have = (700/5) = 140

∴ The average number of Chocobar ice creams they all have is 140.

Calculation:

Here, from the table, we can see, the number of Chocobars is what percent more or less with respect to Cornettos is given

So, we can say, Arun has 20% more Chocobars than Cornettos 

Let, the total number of Cornettos be 100

So, the ratio of Chocobars and Cornettos = (100 + 20) ∶ 100

⇒ 6 ∶ 5

Similarly, we can say the same for others,

So, put those data in a table, we get,

 

The total number of Chocobar ice creams Arun, Kiran and Rumi has = (120 + 180 + 100) = 400

The total number of Cornetto ice creams Barun and Sonal has = (200 + 100) = 300 

So, the ratio will be = 400 ∶ 300 = 4 ∶ 3

∴ The required ratio is 4 ∶ 3.

Calculation:

Here, from the table, we can see, the number of Chocobars is what percent more or less with respect to Cornettos is given

So, we can say, Arun has 20% more Chocobars than Cornettos 

Let, the total number of Cornettos be 100

So, the ratio of Chocobars and Cornettos = (100 + 20) ∶ 100

⇒ 6 ∶ 5

Similarly, we can say the same for others,

So, put those data in a table, we get,

 

The total number of Cornettos all of them have = (100 + 200 + 200 + 80 + 100) = 680

The total number of Chocobars all of them have = (120 + 140 + 180 + 100 + 160) = 700

So, the difference = (700 - 680) = 20

∴ The required difference is 20

Shortcut Trick

Initial Average age = 20 years.

New students' age = 7.5 years each. Deficit per new student = 20 − 7.5 = 12.5 years.

Total deficit for 4 students = 4 × 12.5 = 50 years.

This deficit caused the total average to decrease by 5.

Total number of students (x + 4) = Total deficit ÷ decrease in average = 50 ÷ 5 = 10.

x = 10 − 4 = 6.

∴ The correct answer is 6.

Alternate Method

Given: Initial students = x, Initial average = 20, New students = 4, Age of each = 7.5, New average = 20 − 5 = 15.

Formula Used: Total Age = Number of students × Average Age

⇒ Total initial age = 20 × x

⇒ Age of 4 new students = 4 × 7.5 = 30

⇒ New total students = x + 4

⇒ New total age = 15 × (x + 4)

⇒ 20x + 30 = 15(x + 4)

⇒ 20x + 30 = 15x + 60

⇒ 5x = 30

⇒ x = 6

∴ The correct answer is 6.

Additional Information

Weighted Average Formula

When two groups are combined, the new average is A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Net Deviation Principle

In any average problem, the sum of deviations of all observations from the average is always zero.

Shortcut Trick

Side of large cube (A) = √³(3³ + 4³ + 5³) = √³(27 + 64 + 125) = √³(216) = 6 cm.

Sum of Total Surface Areas (TSA) of small cubes = 6 × (3² + 4² + 5²) = 6 × (9 + 16 + 25) = 6 × 50 = 300 cm².

TSA of large cube = 6 × 6² = 6 × 36 = 216 cm².

Required Ratio = 300 : 216 = 25 : 18.

∴ The correct answer is 25 : 18.

Alternate Method

Given: Sides of three cubes are 3 cm, 4 cm, and 5 cm.

Formula Used: Volume of cube = a³; Total Surface Area = 6a².

⇒ Total Volume = 3³ + 4³ + 5³ = 27 + 64 + 125 = 216 cm³

⇒ Side of large cube (A) = √³(216) = 6 cm

⇒ Sum of TSAs of small cubes = 6(3²) + 6(4²) + 6(5²) = 6(9 + 16 + 25) = 6 × 50 = 300 cm²

⇒ TSA of large cube = 6 × 6² = 216 cm²

⇒ Ratio = 300 : 216

⇒ Dividing by 12: 25 : 18

∴ The correct answer is 25 : 18.

Additional Information

Cube Mensuration

Lateral Surface Area of a cube = 4a² and Diagonal of a cube = a√3.

Conservation of Volume

When objects are melted and recast, the total Volume remains constant (V₁ + V₂ + ... = V_final).

Surface Area Change

Upon melting smaller shapes to form a larger one, the Total Surface Area usually decreases because internal faces are lost.

Shortcut Trick

Speed of Bus = 1330 ÷ 19 = 70 km/h

Speed of Bike = 50% of 70 = 35 km/h

Speed of Cycle = 35 − 15 = 20 km/h

Time Ratio (Cycle : Bike) for same distance = Speed of Bike : Speed of Cycle = 35 : 20 = 7 : 4

∴ The correct answer is 7 : 4.

Alternate Method

Given: Distance = 1330 km, Time = 19 hours, Fixed Distance = 280 km

Formula Used: Speed = Distance ÷ Time; Time = Distance ÷ Speed

⇒ Speed of Bus = 1330 ÷ 19 = 70 km/h

⇒ Speed of Bike = 70 − (50% of 70) = 70 − 35 = 35 km/h

⇒ Speed of Cycle = 35 − 15 = 20 km/h

⇒ Time taken by Cycle = 280 ÷ 20 = 14 hours

⇒ Time taken by Bike = 280 ÷ 35 = 8 hours

⇒ Required Ratio (Cycle : Bike) = 14 : 8 = 7 : 4

∴ The correct answer is 7 : 4.

Additional Information

Inverse Relationship of Speed and Time

When the distance is constant, the time taken is inversely proportional to the speed. Ratio of Speed S₁:S₂ = Ratio of Time T₂:T₁.

Percentage Decrease

If a value is x% less than another value V, the new value is V × (100 − x)/100.

Relative Speed

In the same direction, relative speed is the difference (S₁ − S₂). In opposite directions, it is the sum (S₁ + S₂).

Shortcut Trick

Let Upstream speed be U and Downstream speed be D.

Set 1: 52/U + 42/D = 10 | Set 2: 60/U + 66/D = 13

By inspection or HCF method for D (42, 66), try D = 6 or 14. If D = 14, 42/14 = 3 hours, then 52/U = 7 → U = 52/7 (not integer). If D = 6, not possible for downstream.

Try D = 14 and U = 6. Set 1: 52/6.5 + 42/14 = 8 + 3 = 11 (close). Using Elimination: U = 6.5 km/hr, D = 14 km/hr (approx) or solving: U = 8 km/hr, D = 12 km/hr.

Checking U = 8, D = 12: 52/8 + 42/12 = 6.5 + 3.5 = 10 (Matches!). 60/8 + 66/12 = 7.5 + 5.5 = 13 (Matches!).

Speed in still water = (D + U) ÷ 2 = (12 + 8) ÷ 2 = 10 km/hr.

∴ The correct answer is 10 km/hr.

Alternate Method

Let speed of man be u and speed of current be v. Upstream speed U = u − v, Downstream speed D = u + v.

From given data:

⇒ 52/U + 42/D = 10 ... (i)

⇒ 60/U + 66/D = 13 ... (ii)

Multiply (i) by 15 and (ii) by 13 to equate 1/U terms:

⇒ 780/U + 630/D = 150

⇒ 780/U + 858/D = 169

Subtracting the equations:

⇒ 228/D = 19

⇒ D = 228 ÷ 19 = 12 km/hr

Substitute D = 12 in (i):

⇒ 52/U + 42/12 = 10 ⇒ 52/U + 3.5 = 10 ⇒ 52/U = 6.5

⇒ U = 52 ÷ 6.5 = 8 km/hr

Speed of man in still water = (D + U) ÷ 2

⇒ (12 + 8) ÷ 2 = 20 ÷ 2 = 10 km/hr

∴ The correct answer is 10 km/hr.

Additional Information

Upstream and Downstream formulas

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

Speed of Still Water

Speed of boat in still water = (Downstream speed + Upstream speed) ÷ 2.

Speed of Current

Speed of stream or current = (Downstream speed − Upstream speed) ÷ 2.

Follow BODMAS rule to solve this question, as per the order given below, 

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and follow BODMAS rule in the bracket,

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step - 4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

25.96% of 250.05 + 75.96% of 75.05 + √80.99 = ?

⇒ 26% of 250 + 76% of 75 + √81 = ? 

⇒ 65 + 57 + 9 = ?

⇒ ? = 131

Follow BODMAS rule to solve this question, as per the order given below,

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and follow BODMAS rule in the bracket,

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step - 4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

2.93 × 4.85 - ? - 6.97 × (2.02 + 0.99) = ∛511.9

3 × 5 - x - 7 × (2 + 1) = ∛512

⇒ 3 × 5 - x - 7 × 3 = 8 

⇒ 15 - x - 21 = 8

⇒ -x - 6 = 8

∴ x = -14

Follow BODMAS rule to solve this question, as per the order given below,

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and follow BODMAS rule in the bracket,

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step - 4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

599.99 × 3/2 of 19.92% of (109.99 – 9.99) = ?

= 600 × 3/2 of 20% of 100 = ?

= 600 × 3/2 of 20/100 of 100 = ?

= 600 × 3/2 of 20 = ?

= 600 × 3/2 × 20 = ?

= 600 × 30 = ?

= 18000 = ?

Follow BODMAS rule to solve this question, as per the order given below,

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and follow BODMAS rule in the bracket,

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step - 4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

(2.992 × 3.992× 4.99) ÷ 35.99 = (?)2 – 79.99

⇒ (32 × 42× 5) ÷ 36 = (?)2 – 80

⇒ (?)2 = ((9 × 16 × 5) ÷ 36) + 80

⇒ (?)2 = (720 ÷ 36) + 80

⇒ (?)2 = 20 + 80 = 100

⇒ (?) = √100 = 10

Follow BODMAS rule to solve this question, as per the order given below,

Step - 1: Parts of an equation enclosed in 'Brackets' must be solved first, and follow BODMAS rule in the bracket,

Step - 2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step - 3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step - 4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Since, we need to find out the approximate value,

So, we can write these values to their nearest integers.

Given expression is

324.95 – [(11.99)2 – 74.9] = (?)2 – 67.99

⇒ 325 – [(12)2 – 75] = (?)2 – 68

⇒ 325 – [144 – 75] + 68 = (?)2

⇒ 325 – 69 + 68 = (?)2

⇒ 324 = (?)2

⇒ 18 = ?

The total quantity of wheat and pulses in company P is 

⇒ 300+200 = 500kg

The total quantity of wheat and pulses in company Q is 

⇒ 350+275 = 625kg

Ratio of this quantity of P and Q is 500 : 625

⇒ 500 : 625  = 4 : 5

Hence 4 : 5 is the correct answer.

Quantity of rice in company Q is 200 kg and salts in company Q is 320kg

Total quantity of Rice and Salt ,

⇒ 200+320 = 520kg

Quantity of pulses in company P is 200kg and salts in company P is 180kg 

Total quantity of Pulses and salts 

⇒ 200kg+180kg = 380kg 

Then difference of these quantities 

⇒ 520kg - 380kg 

⇒ 140 kg 

Hence 140 kg is the correct answer.

Total quantity of wheat, rice, pulses and salts in company P is 

⇒ 300kg + 250kg +200kg +180kg 

⇒ 930 kg 

Total quantity of wheat, rice, pulses and salts in company Q is 

⇒ 350kg +200kg + 275kg + 320kg = 1145kg

⇒ 1145kg - 930kg = 215kg 

⇒ ( 215kg / 1145kg ) × 100

⇒ 18.77%~ 19% less than the company Q

Hence 19% less is the correct answer.

Quantity of Salts sold by company P and Q together is 

⇒ 180kg + 320kg 

⇒  500 kg 

Quantity of wheat sold by company P is 

⇒  300 kg 

Difference in quantity is 

⇒ 500kg - 300kg 

⇒ 200 kg 

Hence 200 kg is the correct answer.

The total quantity of wheat, rice, pulses and salts sold by companies P and Q in the month of January is 

 ⇒ 2075 kg 

 In the month of February quantity is 20% more than the month of January is 

 ⇒ 20% = 1/ 5

 ⇒ 5 unit = 2075 kg 

 Then, quantity of P and Q in the month of February is 5 unit + 1 unit = 6 unit 

 ⇒ 1 unit = 415 kg 

 Then, 6 unit = 2490 kg 

 Hence 2490 kg is the correct answer.

An uncertain number of people are sitting in a row facing north and are at an equal distance between them.

1. Only one person is sitting between D and I, who is sitting fourth from the left end.

Here, we get two possible cases.

                      

2. G is sitting third to the right of D, who is sitting immediate right of A.

3. Two people are sitting between G and F.

                                            

4. The number of people sitting between I and F is the same number of people sitting between F and B.

5. C is sitting exactly between F and B, who is sitting immediate left of H.

6. The number of people sitting to the left of A is the same as to the right of H.

In case I: No one sits to the left of A so, a one sits to the right of H.

In case II: Four people sitting to the right of  A so, four people are sitting to the left of H.

7. H is sitting four places away from E, who is not an immediate neighbour of C.

Case I is eliminated because no one sits to the right of H and E is an immediate neighbour of C.

In case II: E sits fourth to the right of H.

Final arrangement:

I is sitting fifth to the left of G.

The correct answer is 'B'.

An uncertain number of people are sitting in a row facing north and are at an equal distance between them.

1. Only one person is sitting between D and I, who is sitting fourth from the left end.

Here, we get two possible cases.

                      

2. G is sitting third to the right of D, who is sitting immediate right of A.

3. Two people are sitting between G and F.

                                            

4. The number of people sitting between I and F is the same number of people sitting between F and B.

5. C is sitting exactly between F and B, who is sitting immediate left of H.

6. The number of people sitting to the left of A is the same as to the right of H.

In case I: No one sits to the left of A so, a one sits to the right of H.

In case II: Four people sitting to the right of  A so, four people are sitting to the left of H.

7. H is sitting four places away from E, who is not an immediate neighbour of C.

Case I is eliminated because no one sits to the right of H and E is an immediate neighbour of C.

In case II: E sits fourth to the right of H.

Final arrangement:

'E' is sitting at the extreme end.

The correct answer is person 'E'.

An uncertain number of people are sitting in a row facing north and are at an equal distance between them.

1. Only one person is sitting between D and I, who is sitting fourth from the left end.

Here, we get two possible cases.

                      

2. G is sitting third to the right of D, who is sitting immediate right of A.

3. Two people are sitting between G and F.

                                            

4. The number of people sitting between I and F is the same number of people sitting between F and B.

5. C is sitting exactly between F and B, who is sitting immediate left of H.

6. The number of people sitting to the left of A is the same as to the right of H.

In case I: No one sits to the left of A so, a one sits to the right of H.

In case II: Four people sitting to the right of  A so, four people are sitting to the left of H.

7. H is sitting four places away from E, who is not an immediate neighbour of C.

Case I is eliminated because no one sits to the right of H and E is an immediate neighbour of C.

In case II: E sits fourth to the right of H.

Final arrangement:

'25' number of people sitting in a row.

The correct answer is 'A'.

An uncertain number of people are sitting in a row facing north and are at an equal distance between them.

1. Only one person is sitting between D and I, who is sitting fourth from the left end.

Here, we get two possible cases.

                      

2. G is sitting third to the right of D, who is sitting immediate right of A.

3. Two people are sitting between G and F.

                                            

4. The number of people sitting between I and F is the same number of people sitting between F and B.

5. C is sitting exactly between F and B, who is sitting immediate left of H.

6. The number of people sitting to the left of A is the same as to the right of H.

In case I: No one sits to the left of A so, a one sits to the right of H.

In case II: Four people sitting to the right of  A so, four people are sitting to the left of H.

7. H is sitting four places away from E, who is not an immediate neighbour of C.

Case I is eliminated because no one sits to the right of H and E is an immediate neighbour of C.

In case II: E sits fourth to the right of H.

Final arrangement:

F is sitting six places away from D and 'G' is sitting third to the left of F.

The correct answer is 'D'.

An uncertain number of people are sitting in a row facing north and are at an equal distance between them.

1. Only one person is sitting between D and I, who is sitting fourth from the left end.

Here, we get two possible cases.

                      

2. G is sitting third to the right of D, who is sitting immediate right of A.

3. Two people are sitting between G and F.

                                            

4. The number of people sitting between I and F is the same number of people sitting between F and B.

5. C is sitting exactly between F and B, who is sitting immediate left of H.

6. The number of people sitting to the left of A is the same as to the right of H.

In case I: No one sits to the left of A so, a one sits to the right of H.

In case II: Four people sitting to the right of  A so, four people are sitting to the left of H.

7. H is sitting four places away from E, who is not an immediate neighbour of C.

Case I is eliminated because no one sits to the right of H and E is an immediate neighbour of C.

In case II: E sits fourth to the right of H.

Final arrangement:

'15' number of people are sitting between H and A.

The correct answer is 'C'.

The least possible Venn diagram for the given statements is:

Conclusions:

I. Some apples are fruit. → False ( As there is no definite relation between apples and fruit. Therefore this is possible but not definite)

II. Some fruits are bananas. → True (As it is given "Only a few fruits are bananas" therefore some fruits are bananas is true)

Hence, only 2 follows is the correct answer.

The least possible Venn diagram for the given statements is:

Conclusions:

I. All lemons are banana. → False ( No specific information given about lemons and banana, hence, it is possible but not definite.)

II. Some lemons  are not banana. → False ( No specific information given about lemons and banana, hence, it is possible but not definite.)

Both of the above conclusions are following the conditions of 'either -or' pair.

Hence, either I or II follows.

Additional Information

 Conditions of Either-or case:

1. The elements should be the same in both the statements.
2. Both the conclusions should be false individually.
3. One conclusion should be positive and one conclusion should be negative (Complementary pair)

The two complementary pairs are:

1. All + Some not

2. No + Some

Note: Some + Some not is not  considered under Either -or case.

The least possible Venn diagram based on the given statement is:

Conclusions:

I. Some tree are bird. → False (Nothing specific about tree and bird is given, hence this condition is possible but not definite.)

II. Some pigeon are bird. → False (Nothing specific about pigeon and bird is given, hence this condition is possible but not definite.)

Hence, none follows.

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

Conclusions:

I. Some Copper is Gold → False (As there is no direct relation between copper and gold and some copper is gold is possible but not definite. So, it is false)

II. All Bronze is Copper → False (As there is no direct relation between bronze and copper and all bronze is copper is possible but not definite. So, it is false)

Hence, Neither I nor II follows.

1. Bag is purchased immediately before perfume.

2. Only two persons bought between L and the one who purchase perfume.

 

3. Three persons bought between the one who purchase chair and the one who purchase table. (thus, case 1 and case 2 considered as false)

 

4. Only two persons bought between the one who purchase wallet and the one who purchase table.

5. Two persons bought between A and the one who bought Chair.

6. G purchase immediately before K but none of them bought Chair.

7. S does not buy wallet.

Hence, Perfume and Table is the right answer.

1. Bag is purchased immediately before perfume.

2. Only two persons bought between L and the one who purchase perfume.

 

3. Three persons bought between the one who purchase chair and the one who purchase table. (thus, case 1 and case 2 considered as false)

 

4. Only two persons bought between the one who purchase wallet and the one who purchase table.

5. Two persons bought between A and the one who bought Chair.

6. G purchase immediately before K but none of them bought Chair.

7. S does not buy wallet.

Hence, S is the right answer.

1. Bag is purchased immediately before perfume.

2. Only two persons bought between L and the one who purchase perfume.

 

3. Three persons bought between the one who purchase chair and the one who purchase table. (thus, case 1 and case 2 considered as false)

 

4. Only two persons bought between the one who purchase wallet and the one who purchase table.

5. Two persons bought between A and the one who bought Chair.

6. G purchase immediately before K but none of them bought Chair.

7. S does not buy wallet.

 

Hence, A purchase perfume is the correct answer.