IBPS PO Prelims Memory Based Paper (Held on:4 December 2021 Shift 3) (Previous Year Paper)

The correct answer is option 2), i.e., Both A and B

Key Points 

The meaning of 'Allusion' is ' the act of making an indirect reference to something'. It is a noun.

Its synonyms are – ‘reference to, citation of, implication, insinuation, etc ‘

• In sentence A, it has been used correctly as ‘allusions in the novel’ means references in the novel that properly fits the context of the sentence.
• In sentence B, it has been used correctly as ‘ allusion to the years’ means reference to the years they lived apart, which makes sense in the context of the sentence.
• In sentence C, the ‘allusion that you are in control of an airplane’ is erroneous as the meaning that is conveyed by the sentence is that the video games create a simulation that gives a false impression of the real world. So, the correct word here should be ‘illusion’ which means ‘a deceptive appearance or impression or an instance or misinterpreted perception of a sensory experience’

Additional Information

• Literary – concerning the writing, study, or content of literature, especially of the kind valued for quality of form
• Echoes –  the repetition in the structure and content of one speaker's utterance by another.
• Prose - written or spoken language in its ordinary form, without metrical structure.

Hence, both A and B best express the meaning of the word.

The correct answer is 'A and B'.

Key Points

• The word 'Borne' means carried or moved by a particular thing.
• Example: The boat has borne away.
• By understanding the meaning of the given word we can get that:
• Sentence A is correct as it is talking about a person being carried to the ambulance.
• Sentence B is correct as it is about someone's story not being carried out well due to facts.
• Sentence C is incorrect as the word borne does not make any sense as per the context of the sentence.
• Hence, the correct answer is option 4.

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

Key Points

• The meaning of the word 'corroborate' is to add proof to an account, statement, idea, etc. with new information.
• Example: If you're going to be my witness, your story must corroborate my story.
• By understanding the meaning of the given word we can get that:
• Sentence A is correct as it talks about recent research which has added new information to a theory.
• Sentence B is correct as the employment trends work as proof against the dismal economy.
• Sentence C is correct as it talks about the subject's story about the disturbance in the lounge and that there was no witness or no one to provide proofs regarding the disturbance.
• Hence, option 3 is the correct answer.

The correct answer is: The wide range of mental and neurological disorders in patients with milder symptoms.  

Key Points

Reading the given passage we find that: 

'However, what is alarming is the wide gamut of mental and neurological disorders seen even in those with milder symptoms.'

Thus from the given sentence, it is clear that the correct answer is option 4.

The correct answer is: Enormous 

Key Points

Let's look at the meaning of the given word. 

• Gargantuan: Enormous.

Thus from the above meaning, it is clear that the correct answer is Enormous. 

Additional Information

• Puny: small and weak.
• Miniscule: extremely small, tiny.
• Tepid: slightly warm; lukewarm.
• Opulent: costly and luxurious.

The correct answer is: Confinement. 

Key Points

Let's look at the meaning of the correct answer. 

• Confinement: The action of confining or the state of being confined.
• The given sentence talks about state of confinement people experience while staying home.

Therefore the correct answer is Confinement**.**

The correct answer is: All of the above. 

Key Points

Reading the given passage we find the following lines:  

• 'It has been hypothesized that the causative mechanism for many of the neurological conditions due to COVID-19 may be the direct invasion of the nervous system by the virus, an increased tendency to blood clotting or an exaggerated immune response by the body.'
• Thus from the given points, we find that direct invasion of the nervous system, increased tendency to blood clotting, and an exaggerated immune response by the body all arise due to the neurological conditions due to COVID-19.

Therefore the correct answer is All of the above.

The correct answer is Operate. 

Key Points

Let's look at the meaning of the given word and the correct option: 

• Function: Work or operate in a particular way.
• Operate: Control the functioning of something.

Thus from the given meaning, it is clear that the correct answer is Operate. 

Additional Information

• Conjugate: Become temporarily united (biological term).
• Impede: Delay or prevent by obstructing.

The correct answer is: Smoking and consumption of alcohol decreased due to prolonged quarantine. 

Key Points

Reading the passage we find that:  

• **'**There was a steep increase in the amount of alcohol consumed by regular drinkers. Persons who had stopped smoking and consuming alcohol resumed their habit in disconcerting numbers.'

Here from the given sentence, it is clear that the statement given in the option is false. 

Therefore the correct answer is Smoking and consumption of alcohol decreased due to prolonged quarantine.

The correct answer is: The imposed virtual learning has increased the mental stress and fatigue in students. 

Key Points

Reading the sentence we find that:  

'Mental stress and fatigue have increased manyfold due to the rigours imposed by virtual learning.'

Thus from the given line, it is clear that virtual learning has increased mental stress and fatigue in students. 

All the other points mentioned in the options are wrong and is not mentioned in the passage.

The correct answer is: Both 1 and 3.

Key Points

Reading the passage we find that:  

• 'Remote working disrupts a healthy-work life balance. Face to face contact and human interactions which were considered so essential for emotional well-being has taken a backseat. Lack of comforting physical contact like shaking hands and hugging friends is stressful and disconcerting.'

Therefore the correct answer is Both 1 and 3 as we see both the points are mentioned in the passage.

The correct answer is Agreement. 

Key Points

Let's look at the meaning of the given word.

• Accord: Be harmonious or consistent with.
• Agreement: Having the same opinion about something.

Thus from the given meanings, it is clear that the correct answer is Agreement.  

Additional Information

Transpose: Cause two things to exchange places

The correct answer is Weakness that could result in failure.

Key Points

• 'Achilles heal' means 'weakness or vulnerable point that can lead to failure'.
• For example, The country's dependence on imported oil could prove to be its Achilles' heel if prices keep on rising.
  

Therefore, option 1 is the correct answer.

The idiom, 'to be in the doldrums' means 'to be depressed, low spirited or sluggish'. The use of the idiom can be seen in the following sentence: Harry has been in the doldrums ever since he lost his job as a print journalist.

The correct answer is Option 4) i.e. Only A-D.

Key Points

• If we go through the given statement, it is not correct since it does not make any sense.
• Though it may seem that with some changes, the sentence would imply something.
• Here, we have to understand the context of the statement which is talking about the action to be taken by the Union Minister against others.
• Now, coming to the options, Option 1 can be ruled out since it is clear that with this option being implemented, the resultant statement would not make any sense whatsoever.❌
• With Option 2 also, the same may be said since it also does not make any sense.❌
• Option 3 can be ruled out since it does imply anything.❌
• Option 4 is the right pick since if we interchange the words according to this option, the resultant statement will make sense.​ 'Threatened' should be used along with the term 'legal action', and with further part of the sentence 'two newspapers' fitting in well.

Correct sentence: Union minister M.J. Akbar threatened to take legal action against several women journalists who had accused him of sexual harassment at two newspapers where he had been the editor.✔️

The correct answer is CBAD

Key Points

From the context of the sentence, we can see that Vikram was a certain way because of which something happened to chinaware. 

• Let's look at the meaning of the words:

• Now let's assume that the emboldened words in the sentence have been replaced with blank spaces:
• Vikram was very __________with his handling of the ___________, he ended up __________most of the pieces before they even __________.
• The first blank requires an adjective that can be used to describe the kind of person Vikram is in terms of handling something. 
• 'Reckless' is an adjective that describes someone who is careless and does not give much thought to how they do things.
• The third blank requires a verb that can describe the action taken by Vikram on the chinaware. 
• 'Demolishing' is a verb that describes destroying something or destructing it, which is very much possible if a person is careless or irresponsible.
• Hence, the terms 'demolishing' and 'reckless' need to be interchanged in order to make the sentence grammatically and contextually correct.
• Thus, The correct sentence will be: Vikram was very reckless with his handling of the chinaware, he ended up demolishing most of the pieces before they even turned up.

So, the correct  answer is CBAD

The correct answer is B-C.

Key Points

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

The ____ (A) was a page five ____ (B) and ____ (C) will be ____ (D) in a couple of days.

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

• From the above meanings it is clear that
• page five hopefully is an incorrect phrase.
• and filler will be is also incorrect.
• So, B and C should be interchanged to make the sentence correct.

Therefore the correct sentence is - The article was a page five filler and hopefully will be forgotten in a couple of days.

The correct answer is A-C.

Key Points

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

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

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

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

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

Hint

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

The correct answer is No rearrangement.

Key Points

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

He ____ (A) her up and she ____ (B) to stand, but her ____ (C) felt like ____ (D).

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

• From the above meanings it is clear that all words are in their correct places.
• The sentence implies that someone tried to stand up with the help of another person but her legs were not cooperating.
• So, there is no rearrangement of the words.

The given sentence talks about the waste management of Europe and North America. So here the correct word that should be used is ‘effective’ which means successful in producing the desired or intended result. So option 1 is the correct answer.

Here the given sentence talks about the face of waterways. So out of the given options, ‘pristine’ which means clean and fresh is the correct word that should be used here. So option 3 is the correct answer.

Here the given sentence talks about the plastic particles that are polluting the ocean and thus affecting the human life and eco systems. So here the correct word that should be used is ‘impacting’ which means have a strong effect on someone or something. Thus, option 4 is the correct answer.

Key Points

• The given sentence here talks about the images of countryside garbage patches floating in the ocean which was something bad to see. So to express this correct word is ‘shocking’ which means causing a feeling of surprise and dismay.
• So option 2 is the correct answer.

Mistake Points

• The word 'horrifying' also mean 'very shocking' but since the context of the given sentence focuses on the images of countryside garbage patches floating in the ocean, the word 'shocking' fits more appropriately.

Additional Information

• Let's look into the meaning of the words given in the options:
• Repelling: Be repulsive or distasteful to.
• Example: Her arrogance repels many people.
• Bewildering: To confuse someone.
• ​Example: The instructions completely bewildered me.
• Offensive: Causing someone to feel resentful, upset, or annoyed.
• ​Example: The allegations made are deeply offensive to us.

Here the given sentence talks about the strategy that needs to be followed for proper waste management. So the most suitable word that should fit here is ‘address’ which means to focus on a particular issue. So option 5 is the correct answer.

The correct answer is A-E.

Key Points

We need to join the sentence segments in column 1 with those in column 2 to create sentences that are contextually and grammatically correct. Let us see how the parts of the sentence can join.

• PART A joins with PART E to make a contextually correct sentence. Part A states that the local officials were asked to do something and Part E explains what they were asked to do.(remove anything lying in the streets that could be used as projectiles)
• Rest of the combinations don't make sense.

In the given options, the correct answer is A-E reflected in option 3, making it the correct answer.

Additional Information

• Superior: higher in rank, status, or quality
• Projectile: a missile for a weapon (such as a firearm)
• Indeed: really or certainly, often used to emphasize something

Confusion Points

Note: In the street vs On the street

• 'In the street' is used to describe an action taking place on the surface of the street itself, in the space between houses or sidewalks.
• 'On the street' is used to describe a location that is not physically in the middle of the street, but is at the side of the street, or even a house or a building beside a specific street.

The given sentence implies removal of things lying (describing an action) around which could be used as projectiles. So, the correct usage is 'in the street'.

The correct answer is B-F

Key Points

We need to join the sentence segments in column 1 with those in column 2 to create sentences that are contextually and grammatically correct. Let us see how the parts of the sentence can join.

• PART B & PART F can be used to form a single sentence as PART B talks of a dream and PART F justifies it by stating that he should remember them.
• PART A has the subject 'we', but none of the options in column 2 actually have a plural subject.
• PART C is a complete sentence itself and would require a conjunction in the next part. PART B has a conjunction but B and C can't be formed together.(both belong to the same column)
• PART B has a conjunction which means the next part of B should start with a noun or pronoun. PART F stars with the pronoun 'he'. So, B & F go together.

In the given options, the correct answer is B-F reflected in option 4, making it the correct answer.

Additional Information

• Pleased: happy or satisfied about something
• Desire: the feeling of wanting something very much; a strong wish
• Excited: feeling or showing happiness and enthusiasm; not calm
• Occasion: a particular time when something happens
• Remember: to have somebody/something in your mind or to bring somebody/something back into your mind

The correct answer is A-E, B-F and C-D.

We need to join the sentence segments in column 1 with those in column 2 to create sentences that are contextually and grammatically correct. Let us see how the parts of the sentence can join.

• Part A and Part E: Part A  talks about the strict implementation of The Consumer Protection Act and Part E justifies its implementation by saying "so that the businessmen become alert and are compelled to stop unfair trade practice". Hence, these two fragments can be combined together to form a sentence both meaningful and grammatically correct. This pair is correct.
• Part B talks about the music industry being saturated with too many singers and Part F shows the effect of having so many singers by saying that the lifetime of a singer is hence reduced to one or two songs only. These two fragments can also be combined in order to form a meaningful statement both contextually and grammatically correct.
• Part C talks about the showbiz business not being as rosy as it seems and Part D specifies the dark sides to it once you enter into this. Thus, These two fragments can be combined to form a grammatically and contextually correct sentence. This pair is hence correct.

In the given options, the correct answers A-E, B-F and C-D are reflected in option 3, making it the correct answer.

• Saturated: to fill a place or a thing completely so that no more can be added
• Implement: to start using a plan or system
• Rosy: pleasant in appearance or full of good possibilities

The underlined part of the sentence is grammatically incorrect. The preposition 'for’ used here is wrong. The correct preposition should be 'to’.

Gauge means to judge or assess (a situation, mood, etc.). Hence 'assess’ is a synonym of 'gauge’.

Both choices B and C are correct.

Hence the correct answer is option 4.

The correct answer is Insolence.

Key Points

We have to choose the word which is similar to the emboldened word and replace it.

• Audacity: willingness to take bold risks; rude or disrespectful behaviour; impudence.
• Insolence: rude and disrespectful behaviour

Additional Information

Let's take a look at the meaning and usage of the words given in the question and options-

• Cowardice: lack of bravery
• He openly accused his opponents of cowardice.
• Presumption: an idea that is taken to be true on the basis of probability
• The woman completed her workday even though there was a presumption that she was to be fired.
• Brevity: concise and exact use of words in writing or speech.
• ​You did a good job on the brevity of this newsletter this week.
• Heed: pay close attention to
• The union failed to heed warnings that strike action would lead to the closure of the factory.

Therefore, from the given options, the best alternative for the emboldened word is 'Insolence'.

The correct answer is 'Assign'.

Key Points

• The word "consign" means put someone or something in (a place) in order to be rid of it or them and "assign" means designate or set (something) aside for a specific purpose.
• Therefore, "consign" can be replaced with "assign" in the sentence, without changing its meaning.
• Hence, 4 is the correct option.

Additional Information

• Let's look at the meanings of all the other words given in the option:
• Announce: make a formal public statement about a fact, occurrence, or intention
• Circulate: move continuously or freely through a closed system or area
• Indicate: point out; show

The series follows the following pattern:

64 – 2 = 62

62 + 3 = 65

65 – 5 = 60

60 + 7 = 67

67 – 11 = 56 

Important point:

subtraction and addition is done by prime numbers in this series

Given:

The number series:

6, 8, 11, 16, 23, ?

Concept Used:

Prime numbers = 2, 3, 5, 7, 11,....

A prime number is a number that does not any other factor other than 1 and the number itself.

Calculation:

The series follows the following pattern:

6 + 2 = 8

8 + 3 = 11

11 + 5 = 16

16 + 7 = 23

23 + 11 = 34

∴ The required number in the place of "?" in the given series is 34

prime number has been added to each number

The series follows the following pattern:

8.5 × 1 + 1 = 9.5

9.5 × 2 + 2 = 21

21 × 3 + 3 = 66

66 × 4 + 4 = 268

268 × 5 + 5 = 1345

The series follows the following pattern:

29 + 12 = 30

30 - 22 = 26

26 + 32 = 35

35 - 42 = 19

19 + 52 = 44

The series follows the following pattern:

77 – 1 = 76

76 + 8 = 84

84 – 27 = 57

57 + 64 = 121

121 – 125 = – 4

∴ The missing term in the series is 121.

The series follows the following pattern:

0.25 × 1 + 1 = 1.25

1.25 × 2 + 2 = 4.5

4.5 × 3 + 3 = 16.5

16.5 × 4 + 4 = 70

70 × 5 + 5 = 355

Percentage of Scale 1 officers in Banks D, E, and F are 24%, 14%, and 10% respectively.

∴ Average number of Scale 1 officers in Banks D, E and F

= [24 + 14 + 10] / 3 × 1 / 100 × 400

= 16 × 4

= 64

Number of scale I officers in Bank B in January 2015 = 12 / 100 × 400 = 48

Number of scale I officers in Bank D in January 2015 = 24 / 100 × 400 = 96

Suppose the number of female Scale I Officers in the same bank = p

⇒ Number of male Scale I Officers in Bank B = 3p

p + 3p = 48

⇒ p = 12

Number of female Scale I Officers in bank B = 12

⇒ Number of female Scale I Officers in bank D = 12

∴ Number of male Scale I Officers in bank D = 96 - 12 = 84

Number of scale I officers in Bank B in January 2015 = 12 / 100 × 400 = 48

Number of scale I officers in Bank D in January 2015 = 24 / 100 × 400 = 96

Number of scale I officers in Bank E in January 2015 = 14 / 100 × 400 = 56

⇒ Number of unmarried scale I officers in Banks B, D and E together = (48 + 96 + 56) × 32 / 100

= 64

∴ Number of unmarried Scale I officers in Bank D = 64 × 2 / 8 = 16

Number of Scale 1 officer in bank A in January 2015 = 400 × 15 / 100 = 60

⇒ Number of Scale 1 officer recruited in December 2014 = 60 - 44 = 16

Given: In December 2014, 4% of the candidates who applied for a job as Scale 1 officer were recruited in Bank A.

∴ Number of candidates who applied for the job = 16 / 4 × 100 = 400

Number of scale I officers in Bank B in January 2015 = 12 / 100 × 400 = 48

Number of scale I officers in Bank C in January 2015 = 25 / 100 × 400 = 100

Suppose ‘a’ number of Scale I Officers resigned from Bank C and all of them joined Bank B in January 2016.

⇒ (100 - a) : (48 + a) = 24 : 13

⇒ 1300 - 13a = 1152 + 24a

⇒ 37a = 148

⇒ a = 4

∴ Number of Scale I Officers who resigned from Bank C = 4

I. x2 + 7x + 10 = 0 

⇒ x² + 5x + 2x + 10 = 0

⇒ x(x + 5) + 2(x + 5) = 0

⇒ (x + 2) (x + 5) = 0

⇒ x = -2, -5

II. y2 + 5y + 4 = 0

⇒ y² + 4y + y + 4 = 0

⇒ y(y + 4) + 1 (y + 4) = 0

⇒ (y + 4) (y + 1) = 0

⇒ y = -4, -1

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

Calculations:

I. x² + 35x + 306 = 0

⇒ x² + 17x + 18x + 306 = 0

⇒ x(x + 17) + 18(x + 17) = 0

⇒ (x + 17) (x + 18) = 0

⇒ x = -17, -18

II. y² + 41y + 408 = 0

⇒ y² + 17y + 24y + 408 = 0

⇒ y(y + 17) + 24(y + 17) = 0

⇒ (y + 17) (y + 24) = 0

⇒ y = -17, -24

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

i. x² - 19x + 60 = 0

⇒ x² - 15x - 4x + 60 = 0

⇒ (x - 15) (x - 4) = 0

⇒ x = 15, 4

ii. y² - 20y + 99 = 0

⇒ y² - 11y - 9y + 99 = 0

⇒ (y - 11) (y - 9) = 0

⇒ y = 11, 9

Hence, Relation between x and y can’t be determine here.

i. x² - 28x + 195 = 0

⇒ x² - 15x - 13x + 195 = 0

⇒ (x - 15) (x - 13) = 0

⇒ x = 13, 15

ii. y² - 21y + 108 = 0

⇒ y² - 12y - 9y + 108 = 0

⇒ (y - 12) (y - 9) = 0

⇒ y = 9, 12

Hence, x > y.

I. x² + 19x + 78 = 0

⇒ x² + 6x + 13x + 78 = 0

⇒ x (x + 6) + 13 (x + 6) = 0

⇒ (x + 6) (x + 13) = 0

⇒ x = -13, -6

II. 45y² + 83y + 28 = 0

⇒ 45y²   + 63y + 20y + 28 = 0

⇒ 9y (5y + 7) + 4 (5y + 7) = 0

⇒ (5y + 7) (9y + 4) = 0

⇒ y = -7/5, -4/9

∴ x < y

I. x² + 31x + 240 = 0

⇒ x² + 15x + 16x + 240 = 0

⇒ x (x + 15) + 16(x + 15) = 0

⇒ (x + 15) (x + 16) = 0

⇒ x = -15, -16

II. 5y² + 60y + 135 = 0

⇒ 5y²   + 45y + 15y + 135 = 0

⇒ 5y (y + 9) + 15 (y + 9) = 0

⇒ (y + 9) (5y + 15) = 0

⇒ y = -9, -3

Hence, x < y

Shortcut Trick

Total Savings = (5 × 2120) + (3 × 4260) + (4 × 3140)

Total Savings = 10600 + 12780 + 12560 = Rs. 35940

Total Expenditure = 12 × 11000 = Rs. 132000

Total Income = Total Savings + Total Expenditure = 35940 + 132000 = Rs. 167,940

∴ The correct answer is Rs. 167,940.

Alternate Method

Given: Average savings for 5, 3, and 4 months; average expenditure for 12 months.

Formula Used: Total = Average × Number of Months; Income = Savings + Expenditure

⇒ Savings_(1-5) = 5 × 2120 = Rs. 10,600

⇒ Savings_(6-8) = 3 × 4260 = Rs. 12,780

⇒ Savings_(9-12) = 4 × 3140 = Rs. 12,560

⇒ Total Annual Savings = 10600 + 12780 + 12560 = Rs. 35,940

⇒ Total Annual Expenditure = 12 × 11000 = Rs. 132,000

⇒ Total Annual Income = 132000 + 35940 = Rs. 167,940

∴ The correct answer is Rs. 167,940.

Additional Information

Weighted Average Savings

The combined average for the year can be found using (n₁x₁ + n₂x₂ + n₃x₃) ÷ (n₁ + n₂ + n₃).

Income Expenditure Relation

In financial math, Income = Expenditure + Savings. This applies to both monthly and annual totals.

Average Concept

Average = Total Sum ÷ Number of observations. To find the sum, multiply the average by the count.

Shortcut Trick

Total students speaking at least one language = 100% − 28% = 72%.

Speaking both languages = (Hindi % + English %) − Total speaking %.

⇒ (60% + 70%) − 72% = 130% − 72% = 58%.

∴ The correct answer is 58%.

Alternate Method

Given: Students speaking Hindi (n(H)) = 60%, English (n(E)) = 70%, Neither = 28%.

Formula Used: n(H ∪ E) = n(H) + n(E) − n(H ∩ E)

⇒ Total Students = 100%

⇒ Students speaking at least one language n(H ∪ E) = 100% − 28% = 72%

⇒ 72% = 60% + 70% − n(H ∩ E)

⇒ 72% = 130% − n(H ∩ E)

⇒ n(H ∩ E) = 130% − 72% = 58%

∴ The correct answer is 58%.

Additional Information

Venn Diagram for Two Sets

The union of two sets A and B is given by n(A ∪ B) = n(A) + n(B) − n(A ∩ B), representing students in at least one category.

Complement of a Set

The percentage of students who do neither activity is 100% − n(A ∪ B).

Only Category Calculations

To find students speaking only Hindi, subtract the intersection from the Hindi total: n(H) − n(H ∩ E).

Shortcut Trick

Equate the total capacity of both glasses by taking LCM of denominators (5 and 4) = 20 units.

Glass 1: Alcohol = 2/5 × 20 = 8 units, Water = 20 − 8 = 12 units.

Glass 2: Alcohol = 1/4 × 20 = 5 units, Water = 20 − 5 = 15 units.

Total: Alcohol = 8 + 5 = 13 units, Water = 12 + 15 = 27 units.

∴ The correct answer is 13 : 27.

Alternate Method

Given: Two equal glasses. Glass 1 alcohol fraction = 2/5. Glass 2 alcohol fraction = 1/4.

Formula: Ratio = (Sum of Alcohol) : (Sum of Water)

⇒ Let the capacity of each glass be 1 unit.

⇒ Total Alcohol = 2/5 + 1/4 = (8 + 5) / 20 = 13/20

⇒ Total Water in Glass 1 = 1 − 2/5 = 3/5

⇒ Total Water in Glass 2 = 1 − 1/4 = 3/4

⇒ Total Water = 3/5 + 3/4 = (12 + 15) / 20 = 27/20

⇒ Required Ratio = (13/20) : (27/20) = 13 : 27

∴ The correct answer is 13 : 27.

Additional Information

Mixture Equality Principle

When two mixtures of equal volume are mixed, the final concentration is the arithmetic mean of the individual concentrations of the components.

Alligation Method

Used to find the ratio in which two mixtures are mixed to get a desired concentration. In this question, since quantities are equal, the ratio of mixing is 1 : 1.

Compound Ratio

The compound ratio of a : b and c : d is (a × c) : (b × d). This is useful when dealng with successive dilutions or multiple vessels of different sizes.

Shortcut Trick

Difference in delay = 42 − 22 = 20 min.

This 20 min difference is caused by covering the 40 km extra distance at original speed instead of reduced speed.

Speed ratio = 3 : 2 → Time ratio = 2 : 3. Difference = 1 unit.

1 unit = 20 min ⇒ Original time for 40 km = 2 units = 40 min = 2/3 hr.

Original Speed = Distance ÷ Time = 40 ÷ (2/3) = 60 km/hr.

∴ The correct answer is 60 km/hr.

Alternate Method

Given: Accident 1 at 100 km, Delay = 42 min. Accident 2 at 140 km, Delay = 22 min. Reduced speed = 2/3 of original speed.

Formula: Time = Distance / Speed | Delay = Time_slow − Time_normal

⇒ Let original speed be s and normal time to cover 40 km be t.

⇒ Reduced speed = (2/3)s, so slow time = t ÷ (2/3) = 1.5t.

⇒ Reduction in delay = (Time_slow − Time_normal) for 40 km distance.

⇒ 42 − 22 = 1.5t − t

⇒ 20 min = 0.5t

⇒ t = 40 min = 40/60 hr = 2/3 hr.

⇒ Original speed s = Distance / t = 40 / (2/3) = 60 km/hr.

∴ The correct answer is 60 km/hr.

Additional Information

Speed-Time Inversity

When distance is constant, speed and time are inversely proportional. If speed becomes a/b, time becomes b/a of the original time.

Accident Case Logic

The difference in time delay is solely due to the distance shifted between the two potential accident spots being covered at different speeds.

Shortcut Trick

Ratio of Downstream speed (D) to Upstream speed (U) = 18 : 14 = 9 : 7.

Let speed D = 9x and U = 7x. Total time = 63/9x + 63/7x = 7/x + 9/x = 16/x.

Given 16/x = 16 hours ⇒ x = 1.

Downstream speed = 9 km/hr, Upstream speed = 7 km/hr.

Speed of stream = (9 − 7) ÷ 2 = 1 km/hr.

∴ The correct answer is 1 km/hr.

Alternate Method

Given: Total distance = 63 km, Total time = 16 hours, Ratio of speeds = 18:14.

Formula Used: Speed = Distance ÷ Time; Speed of stream = (Downstream − Upstream) ÷ 2.

⇒ Ratio of Downstream Speed (D) : Upstream Speed (U) = 18 : 14 = 9 : 7.

⇒ Let D = 9x and U = 7x.

⇒ Total time = (Distance ÷ D) + (Distance ÷ U) = 16.

⇒ 63 ÷ 9x + 63 ÷ 7x = 16.

⇒ 7/x + 9/x = 16 ⇒ 16/x = 16 ⇒ x = 1.

⇒ Downstream speed = 9 km/hr and Upstream speed = 7 km/hr.

⇒ Speed of stream = (9 − 7) ÷ 2 = 2 ÷ 2 = 1 km/hr.

∴ The correct answer is 1 km/hr.

Additional Information

Speed in Still Water

The speed of the boat in still water is the average of downstream and upstream speeds: B = (D + U) ÷ 2.

Speed of Stream

The speed of the current or stream is half the difference between downstream and upstream speeds: S = (D − U) ÷ 2.

Time and Speed Relation

When distance is constant, time is inversely proportional to speed: T₁ ÷ T₂ = S₂ ÷ S₁.

Shortcut Trick

Ratio of Profit Share = (Investment × Time period).

A's ratio = (8000 × 8) + (4000 × 4) = 64000 + 16000 = 80000.

B's ratio = (6000 × 8) + (15000 × 4) = 48000 + 60000 = 108000.

C's ratio = (12000 × 4) = 48000.

Simplified ratio A : B : C = 80 : 108 : 48 = 20 : 27 : 12.

Since 20 units = Rs. 8000, 1 unit = Rs. 400. Share of C = 12 × 400 = Rs. 4800.

∴ The correct answer is Rs. 4800.

Alternate Method

Given → Initial Investments: A = Rs. 8000, B = Rs. 6000. Time = 1 year (12 months). Changes occur after 8 months. Formulas: Profit Ratio = (I₁ × T₁) : (I₂ × T₂) : (I₃ × T₃)

⇒ A's total investment-month = (8000 × 8) + (4000 × 4) = 80000. ⇒ B's total investment-month = (6000 × 8) + (6000 + 1.5 × 6000) × 4 = 48000 + 15000 × 4 = 108000. ⇒ C's total investment-month = 12000 × (12 − 8) = 12000 × 4 = 48000. ⇒ Profit Ratio A : B : C = 80000 : 108000 : 48000 = 20 : 27 : 12. ⇒ Given A's profit = Rs. 8000. ⇒ 20 units = 8000 ⇒ 1 unit = 400. ⇒ C's profit = 12 units = 12 × 400 = 4800.

∴ The correct answer is Rs. 4800.

Additional Information

Partnership Basics

In a partnership, the profit is distributed in the ratio of the product of Investment and Time.

Investment Changes

If an investor changes their capital during the period, calculate the equivalent capital for 1 month by summing (Amount × Duration) for each phase.

No. of people tested positive in July = 48149

Total people tested positive = 7% of 1200000 = 84000.

∴ Required percentage = (48149 ÷ 84000) × 100 = 57.32%

Number of people tested positive in August from Mumbai = (50% of 1200000) – 230068 = 369932

Number of people tested positive in July from Chennai = 147890

∴ Required average = (369932 + 147890)/2 = 258911

Total number of case in July = 230068 + 48149 + 83468 + 147890 = 509575

Total number of case in August = 1200000 – 509575 = 690425

∴ Difference = 690425 – 509575 = 180850

Total people tested positive in Delhi = 7% of 1200000 = 84000

Total people tested positive in Mumbai = 50% of 1200000 = 600000

∴ Required percent = (84000 ÷ 600000) × 100 = 14%

People recovered in the month of July = 70% of 147890 = 103523

People Died in the month of July = 10% of 147890 = 14789

∴ Active cases = 147890 – 103523 – 14789 = 29578

Shortcut Trick

Total Expenditure ratio = 5 : 6

Cost per book ratio = 96 : 120 = 4 : 5

Number of books ratio = (Total Expenditure / Cost per book) = (5/4) : (6/5) = 25 : 24

Given 25 units = 200 books ⇒ 1 unit = 8 books

Number of books in 2018 = 24 units = 24 × 8 = 192 books

∴ The correct answer is 192 books.

Alternate Method

Given:

Cost per book (2013) = Rs. 96 | Cost per book (2018) = Rs. 120

Books printed (2013) = 200

Ratio of Total Expenditure (2013 : 2018) = 5 : 6

Calculations:

⇒ Total Expenditure (2013) = Cost × Quantity = 96 × 200 = Rs. 19200

⇒ According to ratio: 5 units = Rs. 19200

⇒ 1 unit = 19200 ÷ 5 = Rs. 3840

⇒ Total Expenditure (2018) = 6 units = 6 × 3840 = Rs. 23040

⇒ Number of books (2018) = Total Expenditure ÷ Cost per book

⇒ Number of books (2018) = 23040 ÷ 120

⇒ Number of books (2018) = 192

∴ The correct answer is 192 books.

Additional Information

Expenditure Relation

Total Expenditure = Price per unit × Consumption (Quantity). If Price increases, to keep expenditure constant, consumption must decrease.

Ratio Product Rule

If A : B is the ratio of prices and X : Y is the ratio of quantities, then the ratio of total costs is (A × X) : (B × Y).

Shortcut Trick

Total sum ₹45,000 is divided into 4 : 5 ratio.

Small sum = 4/9 × 45,000 = ₹20,000; Large sum = 5/9 × 45,000 = ₹25,000.

CI on ₹20,000 @ 10% for 3 years (Multiplying Factor 1.331) = 20,000 × 0.331 = ₹6,620.

CI on ₹25,000 @ 20% for 3 years (Multiplying Factor 1.728) = 25,000 × 0.728 = ₹18,200.

Total CI = 6,620 + 18,200 = ₹24,820.

∴ The correct answer is ₹24820.

Alternate Method

Given: Total Principal = ₹45,000, Ratio = 4 : 5, Time = 3 years.

Formula Used: CI = P[(1 + R/100)^T − 1]

⇒ Sum 1 (P₁) = 45,000 × (4 / (4 + 5)) = 45,000 × 4/9 = ₹20,000

⇒ Sum 2 (P₂) = 45,000 × (5 / (4 + 5)) = 45,000 × 5/9 = ₹25,000

⇒ CI₁ = 20,000 × [(1 + 10/100)³ − 1] = 20,000 × [1.331 − 1] = 20,000 × 0.331 = ₹6,620

⇒ CI₂ = 25,000 × [(1 + 20/100)³ − 1] = 25,000 × [1.728 − 1] = 25,000 × 0.728 = ₹18,200

⇒ Total CI = CI₁ + CI₂ = 6,620 + 18,200 = ₹24,820

∴ The correct answer is ₹24820.

Additional Information

Effective Rate of Interest for 3 years

For 10%, effective rate is 33.1%. For 20%, effective rate is 72.8%. Calculated using [3R + 3R²/100 + R³/10000]%.

Difference between CI and SI

For 3 years, Difference = PR²(300 + R) / 100³.

Amount in Compound Interest

Amount (A) = P(1 + R/100)ⁿ, where n is the number of years.

Shortcut Trick

Ratio of work done determines the division of money.

Work ratio A : B : C = (6/15) : (6/20) : (remaining work).

A = 6/15 × 800 = ₹320 | B = 6/20 × 800 = ₹240 | C = 800 − (320 + 240) = ₹240.

∴ The correct answer is ₹320, ₹240 and ₹240.

Alternate Method

Given: A finishes in 15 days, B in 20 days. Together they work for 6 days. C finishes the rest in 6 days. Total wage = ₹800.

⇒ Work done by A and B in 6 days = (4 + 3) × 6 = 7 × 6 = 42 units.

⇒ Remaining work done by C = 60 − 42 = 18 units.

⇒ Ratio of work done A : B : C = (4 × 6) : (3 × 6) : 18 = 24 : 18 : 18 = 4 : 3 : 3.

⇒ A share = (4/10) × 800 = ₹320.

⇒ B share = (3/10) × 800 = ₹240.

⇒ C share = (3/10) × 800 = ₹240.

∴ The correct answer is ₹320, ₹240 and ₹240.

Additional Information

Work and Wages Rule

Wages are distributed in the ratio of the actual work done by each person. If everyone works for the same duration, wages are proportional to their efficiencies.

Efficiency Formula

Efficiency = 1 ÷ Time taken. Total Work = Efficiency × Time.

Combined Work

If A and B work together, their combined efficiency is the sum of their individual efficiencies.

Shortcut Trick

Remaining Mixture = 50 − 10 = 40 liters.

In 40 liters, Milk = 40 × (3/5) = 24 liters and Water = 40 × (2/5) = 16 liters.

New Milk = 24 + 12 = 36 liters; New Water = 16 + 12 = 28 liters.

Final Ratio of Water to Milk = 28 : 36 = 7 : 9.

∴ The correct answer is 7 : 9.

Alternate Method

Given: Initial Mixture = 50 liters, Ratio M:W = 3:2.

⇒ After removing 10 liters, Remaining Mixture = 50 − 10 = 40 liters.

⇒ Quantity of Milk in remaining 40L = (3 / (3+2)) × 40 = (3/5) × 40 = 24 liters.

⇒ Quantity of Water in remaining 40L = (2 / (3+2)) × 40 = (2/5) × 40 = 16 liters.

⇒ After adding 12L Milk, Final Milk = 24 + 12 = 36 liters.

⇒ After adding 12L Water, Final Water = 16 + 12 = 28 liters.

⇒ Final Ratio Water : Milk = 28 : 36.

⇒ Dividing both by 4: 28/4 : 36/4 = 7 : 9.

∴ The correct answer is 7 : 9.

Additional Information

Mixture Removal Property

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

Alligation Method

Used to find the proportion in which two or more ingredients at a given price/concentration must be mixed to produce a mixture of a desired price/concentration.

Replacement Formula

Final Quantity = Initial Quantity × (1 − x/V)ⁿ, where x is quantity removed/replaced and V is total volume.

Shortcut Trick

Ratio of Cost Price (CP) to Marked Price (MP) is given by CP : MP = (100 − Discount%) : (100 + Profit%).

CP : MP = (100 − 10) : (100 + 20) = 90 : 120 = 3 : 4.

Given Marked Price = Rs. 8000, so 4 units = 8000.

1 unit = 2000.

Cost Price = 3 units = 3 × 2000 = Rs. 6000.

∴ The correct answer is Rs. 6000.

Alternate Method

Given: MP = Rs. 8000, Discount = 10%, Profit = 20%.

Formulas: SP = MP × (100 − D%) ÷ 100 | CP = SP × 100 ÷ (100 + P%).

⇒ Selling Price (SP) = 8000 × (100 − 10) ÷ 100

⇒ SP = 8000 × 90 ÷ 100 = Rs. 7200.

⇒ Cost Price (CP) = 7200 × 100 ÷ (100 + 20)

⇒ CP = 7200 × 100 ÷ 120 = 60 × 100 = Rs. 6000.

∴ The correct answer is Rs. 6000.

Additional Information

Relationship between CP and MP

The direct formula linking CP and MP is CP/MP = (100 − D%)/(100 + G%), which saves time in exams by bypassing SP calculation.

Profit and Discount Calculations

Profit is always calculated on Cost Price, whereas Discount is always calculated on Marked Price.

Shortcut Trick

Total possible outcomes for 5 dice = 6⁵.

Favorable outcomes for getting different faces = ⁶P₅ = 6 × 5 × 4 × 3 × 2 = 720.

Since 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720, the numerator is 6!.

Probability = 6! / 6⁵.

∴ The correct answer is 6!/6⁵.

Alternate Method

Given: Number of dice = 5. Each die has faces labeled {1, 2, 3, 4, 5, 6}.

Formula Used: Probability (P) = (Favorable Outcomes) / (Total Outcomes)

⇒ Total outcomes for 5 dice = 6 × 6 × 6 × 6 × 6 = 6⁵

⇒ For all faces to be different, the first die can show any of 6 faces, the second any of the remaining 5, the third any of the remaining 4, and so on.

⇒ Favorable outcomes = 6 × 5 × 4 × 3 × 2 = 720

⇒ Note that 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

⇒ Probability = 6! / 6⁵

∴ The correct answer is 6!/6⁵.

Additional Information

Permutations and Combinations

When order matters and items are distinct, use ⁿP_r = n! / (n−r)!. In this case, ⁶P₅ represents picking 5 distinct faces out of 6.

Total Outcomes of Dice

For 'n' standard dice tossed together, the total number of outcomes in the sample space is always 6ⁿ.

Probability Range

Probability of any event E always lies between 0 and 1 (0 ≤ P(E) ≤ 1).

Given:

Side of square = 18 m

Formula used:

Area of square = Side²

Area of circle = πr²

Calculation:

Area of square = Side²

⇒ Area of square park = 18 × 18 = 324 m²

Side of square = 18

⇒ Diameter of circle = 18 + 5 + 5 = 28 m

⇒ Radius of circle = 28 / 2 = 14

⇒ Area of circle = πr² = (22 / 7) × 14 × 14 = 616 m²

Area of the pavement = 616 – 324 = 292 m²

Cost of cementing the pavement is Rs. 15 per m²

∴ Total cost of cementing the pavement = 292 × 15 = Rs. 4380

As per the given information,

1. Julie starts her journey from point ‘Z’ and walks 10km east to reach point ‘Y’

2. then she turns to her left and walks 3km to reach point ‘R’ and,

3. then she turns to her left again and walks 12km to reach point ‘S’.

4. Again, she turns to her left and walks 3km to reach point ‘E’.

5. Finally, she took to her right and moves for another 4km to reach point J.

Therefore, the final diagram is 

Hence, Point E is in the Southwest direction with respect to point R.

As per the given information,

1. Julie starts her journey from point ‘Z’ and walks 10km east to reach point ‘Y’

2. then she turns to her left and walks 3km to reach point ‘R’ and,

3. then she turns to her left again and walks 12km to reach point ‘S’.

4. Again, she turns to her left and walks 3km to reach point ‘E’.

5. Finally, she took to her right and moves for another 4km to reach point J.

Therefore, the final diagram is 

As per the question

Hence, 13Km is the shortest distance between point K and point Y.

As per the given information,

1. Julie starts her journey from point ‘Z’ and walks 10km east to reach point ‘Y’

2. then she turns to her left and walks 3km to reach point ‘R’ and,

3. then she turns to her left again and walks 12km to reach point ‘S’.

4. Again, she turns to her left and walks 3km to reach point ‘E’.

5. Finally, she took to her right and moves for another 4km to reach point J.

Therefore, the final diagram is 

Hence, Point S is to the northwest of Point Z.

Given : MOTIVATION

After changing the vowels to the next letter and the consonants to the previous letter;

LPSJUBSJPM

Hence, there are two letters (P, S, J) in the given words which are repeated more than once.

Given: 945217

By adding 2 in the even digits and subtracting 1 from the odd digits, we will get,

Here can clearly says that 8 and 0 are not repeated.

Therefore, sum of the number = 8 + 0 = 8

Hence, "8" is the correct answer.

According to the given question,

The forward pairs are - EF, TV

The Backward pairs are - EF, CF 

Hence, there are four pairs.

1. Equal number of boxes are kept above and below A
2. Three boxes are kept between A and B

3. The number of boxes kept above B is the same as the number of boxes kept below C.
4. Only two boxes are kept between C and I.

5. One box is kept between A and G, which is not kept immediate above I.

6. No box is kept between F and D, which is not kept above F → D is kept immediately below F
7. E is placed below H, which is kept immediate below D → Case 1 and Case 2 gets canceled because the given statement will not be satisfied.

So, the final arrangement will be

Hence, only two boxes are kept between Fand A.

1. Equal number of boxes are kept above and below A
2. Three boxes are kept between A and B

3. The number of boxes kept above B is the same as the number of boxes kept below C.
4. Only two boxes are kept between C and I.

5. One box is kept between A and G, which is not kept immediate above I.

6. No box is kept between F and D, which is not kept above F → D is kept immediately below F
7. E is placed below H, which is kept immediate below D → Case 1 and Case 2 gets canceled because the given statement will not be satisfied.

So, the final arrangement will be

Hence, A is kept immediately below H.

1. Equal number of boxes are kept above and below A
2. Three boxes are kept between A and B

3. The number of boxes kept above B is the same as the number of boxes kept below C.
4. Only two boxes are kept between C and I.

5. One box is kept between A and G, which is not kept immediate above I.

6. No box is kept between F and D, which is not kept above F → D is kept immediately below F
7. E is placed below H, which is kept immediate below D → Case 1 and Case 2 gets canceled because the given statement will not be satisfied.

So, the final arrangement will be

There are two boxes between I and C, whereas there is only one box between other pairs.

Hence, IC does not belong to the group.

1. Equal number of boxes are kept above and below A
2. Three boxes are kept between A and B

3. The number of boxes kept above B is the same as the number of boxes kept below C.
4. Only two boxes are kept between C and I.

5. One box is kept between A and G, which is not kept immediate above I.

6. No box is kept between F and D, which is not kept above F → D is kept immediately below F
7. E is placed below H, which is kept immediate below D → Case 1 and Case 2 gets canceled because the given statement will not be satisfied.

So, the final arrangement will be

Hence, CB represent the lowermost box and topmost box.

1. Equal number of boxes are kept above and below A
2. Three boxes are kept between A and B

3. The number of boxes kept above B is the same as the number of boxes kept below C.
4. Only two boxes are kept between C and I.

5. One box is kept between A and G, which is not kept immediate above I.

6. No box is kept between F and D, which is not kept above F → D is kept immediately below F
7. E is placed below H, which is kept immediate below D → Case 1 and Case 2 gets canceled because the given statement will not be satisfied.

So, the final arrangement will be

Hence, three boxes are kept between E and H.

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

Conclusions:

I. Some D are not A → False (as there is no direct relation between D and A, it is possible but not definite. So, it is false)

II. Some D are not B → True (as Only a few D are C, and All B are C, some part of D which is not C will not be B. So, it is true)

Hence, Only conclusion II follows.

Confusion PointsPlease note that according to the statement given 'Only a few D are C.' some D will definitely not be C and those D which are not C can not be B either.

Hence, the conclusion 'Some D are not B ' is true.

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

Conclusions:

I. All Sparrow are Parrot → False (as Some Sparrow are Parrot and about the remaining part of Sparrow and Parrot, we cannot say definite relation whether it is true or not. So, it is false)

II. Some Parrot are not Camel → True (as Only a few Parrot are Camel → Some Parrot are Camel and Some Parrot are not Camel. So, it is true)

Hence, Only conclusion II follows.