SBI Clerk Prelims Memory Based Paper (Held On: 10 Jul 2021 Shift 1) (Previous Year Paper)

The correct answer is '(B)'.

Key Points

Reading the sentence we find that:

• The superlative adjective best used in part B is incorrect.
• The sentence is comparing the work of a computer with that of humans.
• Since the comparison is between two objects, we need to use the comparative adjective.
• The sentence can be made correct if we use the comparative adjective better.

The correct sentence will be: A computer can do some tasks better than a person can as humans often make silly mistakes.

Additional Information

• To compare two things, always use a comparative adjective:
• Example: She is the cleverer of the two women.
• To compare three or more things, always use a superlative adjective:
• Example: She is the cleverest of them all.

The correct answer is '(C)'.

Key Points

Reading the sentence we find that:

• The second conjunction therefore used in part C is incorrect.
• We do not repeat conjunctions for the same function.
• The conjunction since  used at the beginning of the sentence joins the two clauses ( Julie was not hungry/ we ate our dinner without her)
• There is no need to use the conjunction therefore.
• The sentence can be made correct if we remove therefore.

The correct sentence will be: Since Julie was not hungry, we ate dinner without her.

Additional Information

• There must not a repetition of conjunction for the same function.
• The only conjunctions that occur in pairs are correlative conjunctions.

The correct answer is '(A)'.

Key Points

Reading the sentence we find that:

• The pronouns used in part A are incongruous.
• Pronouns need to match in number.
• If we is correct then the plural pronoun ourselves should be used.
• If myself is correct then the singular pronoun I should be used.

The correct sentence will be: We shook ourselves / I shook myself dry on the porch and returned to the warmth of the cabin./ 

Additional Information

• Reflexive pronouns are words ending in -self or -selves that are used when the subject and the object of a sentence are the same (e.g., I believe in myself).
• They can act as either objects or indirect objects.
• The nine English reflexive pronouns are myself, yourself, himself, herself, oneself, itself, ourselves, yourselves, and themselves.

The correct answer is '(C)'.

Key Points

Reading the sentence we find that:

• The phrase some them used in part C is incorrect.
• Some is a quantifier while them is a determiner.
• The two needs the preposition of between them for the phrase to be correct.

The correct sentence will be: The pictures were painted by hand, and some of them were very beautiful.

Additional Information

• We must use of between a quantifier and another determiner - I was at a party with some of my friends.

The correct answer is '(C)'.

Key Points

Reading the sentence we find that:

• The pronoun there used in part C is incorrect.
• There is an adverb that means in, at, or to that place or position..
• The sentence can be made correct if we use the pronoun their.

The correct sentence will be: Two children, brother and sister, were on their way to school.

Additional Information

• They're, there, their are often confused. Let us see their meanings and uses - 
• They're is a contraction of they are or they were. - They're (they are) trying to escape from the prison.
• There can be used either as adverb  or a pronoun.
  
• As an adverb it means at that place. It is a location adverb - I can go there to check on your mother.​
  
• As a pronoun it is used to introduce a word or a clause - We know that there are things we need to talk about.
• Their is the third-person plural possessive pronoun. - Their house is next to an open field.

The correct answer is Maintaining. 

Key Points

Reading the given sentence we find that: 

• We need a word that means cause or enable to continue.
• Maintaining:  cause or enable to continue.
• Here the sentence is trying to convey that quality sleep is essential to enable a good mental health.

Therefore the correct answer is Maintaining. 

Additional Information

Foraging: Search wildly for food or provisions.

The correct answer is Relationship. 

Key Points

Here the sentence says that sleep and mental health is connected. 

• Thus we need a word that should convey a similar meaning.
• Relationship: the way in which two or more people or things are connected, or the state of being connected.

Thus from the given meaning, we can conclude that the correct answer is Relationship. 

Additional Information

• Companionship: A feeling of fellowship or friendship.
• Courtship; The romantic period before a couple gets married.

The correct answer is Accepted. 

Key Points

Reading the given segment we find that: 

• We need a word that conveys the meaning 'generally believed or accepted.'
• Accepted: generally believed or recognized to be valid or correct.

Thus from the given meaning, we can conclude that the word accepted is the correct word grammatically and contextually. 

Additional Information

• Focused: Directing a great deal of attention interest or activity.
• Curbed: Restrain or keep in check.
• Adjusted: Alter or move slightly in order to achieve the desired result.

The correct answer is Disruptions.  

Key Points

• The given passage talks about the importance of sleep.
• Let us refer to this line from the passage, *'*Unfortunately, (4)_ in sleep can interrupt these cycles which can impair thinking and emotional regulation.​'
• The blank needs a word that is related to break or problems that affect sleep.
• So, 'disruptions' is the correct word for blank no. 4.

Complete sentence: Unfortunately, disruptions in sleep can interrupt these cycles which can impair thinking and emotional regulation.

The correct answer is Improve.

Key Points

• The given passage talks about the importance of sleep.
• Let us refer to this line from the passage, *'*But sleep doesn’t just ward off risks of mental illness; it also helps (5)_ general mental functions as well. For example: throughout your day, your brain is taking in new information and responding to all kinds of stimuli.​'
• The blank needs a word that means making mental functions better.
• So, 'improve' is the correct word for blank no. 5.

Complete sentence: But sleep doesn’t just ward off risks of mental illness; it also helps improve general mental functions as well. For example: throughout your day, your brain is taking in new information and responding to all kinds of stimuli. 

Additional Information Let's look at the meaning of the other words  -

• Recede -  to go or move away; retreat
• Fade -  to gradually grow faint and disappear.
• Dwindle  - to diminish gradually in size, amount, or strength.
• Intrigue  - to arouse interest.

The correct answer is Accessible. 

Key Points

• The given passage talks about the importance of sleep.
• Let us refer to this line from the passage, '**Then at night, sleep gives your brain the downtime to consolidate and process this information, and commit it to memory so that it’s (6)_ in the future when required.'
• The blank needs a word that means 'able to be reached'
• So, 'accessible' is the correct word for blank no. 6.

Complete sentence: Then at night, sleep gives your brain the downtime to consolidate and process this information, and commit it to memory so that it’s accessible in the future when required.

The correct answer is D-A

Key Points

In the given sentence we should replace D i.e late with A i.e arrived and vice versa to form a coherent sentence. 

• arrived: reached a place at the end of a journey or a stage in a journey
• party: a social gathering of invited guests, typically involving eating, drinking, and entertainment
• over: finished
• late: after the expected, proper, or usual time

Thus, we can see that D-A is the correct rearrangement we need to make the sentence meaningful. 

The correct sentence: We were late to the party and it was almost over when we arrived.

The correct answer is C-B. 

Key Points

Reading the given sentence we find that: 

• The word confines should be replaced with the word house and vice versa.
• This gives us the phrase 'in the confines of the house'
• This means that she had been staying inside her house for a long time that it became her new normal.

Therefore the correct answer is C-B. 

The correct sentence: Her life in the confines of the house became her new normal.

Additional Information

confines: the borders or boundaries of a place, especially with regard to their restricting freedom of movement

The phrase 'new normal' means a current situation, social custom, etc., that is different from what has been experienced or done before but is expected to become usual or typical:

Eg. We are facing a new normal that includes raging forest fires and prolonged drought.

The correct answer is C-B. 

Key Points

Reading the given sentence we find that: 

• The word terrified should be replaced with scary and vice versa.
• A shadow cannot be terrified as it is not a living entity.
• Instead, it can only be scary. But a person can be terrified seeing something scary.
• Therefore we should replace terrified with scary and scary with terrified to get the correct phrase i.e
• 'seeing the scary shadow, she was really terrified.'

Therefore the correct answer is C-B

The correct answer is No change required. 

Key Points

Reading the sentence we find that all the words are correctly placed. 

• accident: an unfortunate incident that happens unexpectedly and unintentionally, typically resulting in damage or injury
• crushed: compressed or squeezed forcefully so as to break, damage, or distort in shape
• depressed: (of a person) in a state of unhappiness or despondency
• agony: extreme physical or mental suffering

 Thus we can see that all the words have already been placed in the correct positions and the given sentence needs no  rearrangement.

The correct answer is B-A. 

Key Points

• lack: the state of being without or not having enough of something
• battle: a sustained fight between large organized armed forces
• concentration: the action or power of focusing all one's attention
• time: the indefinite continued progress of existence and events in the past, present, and future regarded as a whole

Reading the given sentence we find that: 

• Battle should be replaced with lack to form the phrase lack of concentration.
• And the part 'lot of time to battle' indicates his struggle.

Therefore the correct answer is B-A.

The correct answer is D-B. 

Key Points

• came: arrived at a specified place
• occasion: a special or noteworthy event, ceremony, or celebration
• bunch: a number of things, typically of the same kind, growing or fastened together
• conclusion: a judgement or decision reached by reasoning

Reading the given sentence we find that: 

• Conclusion should be there in place of occasion.
• It forms the phrase come to the conclusion.
• And occasion, in the end**,** makes the sentence contextually correct.

Therefore the correct answer is D-B

The correct answer is pilot flew the plane. 

Key Points

• Parallelism is all about balance. The parallel structure shows that two or more items are of the same level of importance within a sentence. For a group of words or phrases to be parallel, they must have the same logical and grammatical structure.
• Since the second part of the sentence is in the past tense, the first part should also be in past indefinite tense.
• Thus, 'pilot flew the plane' is the correct answer.

The correct answer is statue without thinking. 

Key Points

• There are some prepositions that are always followed by a gerund.
• List of such prepositions:
• ​about (in “how about”/ “what about”), after, apart from, because of, before, by, in, in spite of, instead of, on, without
• Examples:
• He told the joke without laughing.
• In spite of studying a lot he didn't pass the exams.
• ​Thus, 'statue without thinking' is the correct answer.

The correct answer is a moment did I

Key Points

• Subject and verb are inverted for expressions beginning with not.
• Therefore I did becomes did I

​Therefore the correct answer is a moment did I.

The correct answer is gave him a bit of advice. 

Key Points

• "An advice" is incorrect because "advice," when used as a single word, is uncountable. It's correct to say "some advice" or "a piece of advice" or "a bit of advice" or "a lot of advice" or "not much advice" etc.
• Example:
• ​As a bit of advice, it may be worth pondering.

The correct answer is No error. 

Key Points

Reading the sentence we find that the correct phrase 'broken out' is used in the sentence. 

• Broken out is the participle form of the phrase break out.
• Break out: (of war, fighting, or similarly undesirable things) start suddenly.

​Therefore the correct answer is No error.

The correct answer is show. 

Key Points

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

• Indicate: To point out; show.
• Show: Allow to be visible; point out.

Thus from the given meanings, we find that both the words are synonyms.  

Therefore the correct answer is show. 

Additional Information

Let's look at the meaning of the other given options. 

• Reject: Dismiss as inadequate.
• Discard: Get rid of something.
• Feel: Experience; be aware of something.
• Ignore: Refuse to take notice.

The correct answer is engrossed. 

Key Points

Let's look at the meaning of the given word and the correct answer. 

• Focused: Directing a great deal of attention or interest.
• Engrossed: Absorb all the interest and attention of.

Thus from the given meanings, we find that both the words have the same meaning and are therefore synonyms. 

Therefore the correct answer is engrossed. 

Additional Information

• Dejected: Sad and depressed.
• Hampered: Hinder or impede the movement.
• Elated: Ecstatically happy.

The correct answer is The wide variety of screams makes it hard. 

Key Points

Reading the passage we find that: 

• It is hard to pin down what defines a scream because: "Though we're pretty good at recognizing a scream when we hear one, the wide variety of screams makes it difficult to pin down what defines them."
• Thus from the emboldened part in the above line, we find that it is hard to define them because of the wide variety of screams.

Therefore we can conclude that the correct answer is 'The wide variety of screams makes it hard.'

The correct answer is 'Explore our pre-linguistic past.'

Key Points

Reading the passage we find the following lines:

• "To study screams is to probe the fuzzy boundary that separates humans from the rest of the animal kingdom. It is a way to explore our pre-linguistic past."

Thus from the given line it is clear that the correct answer is Explore our pre-linguist past.

The correct answer is All of the above. 

Key Points

Reading the above passage we find the following lines:

• '*Understanding its characteristics could improve the treatment of nonverbal patients, help fight crime, or simply make *movies more frightening.**'
• Thus from the above line, we find that all the points mentioned in the options are present in the passage.

Therefore the correct answer is All of the above.

The correct answer is To determine the acoustic qualities that differentiate fearful screams. 

Key Points

Reading the above passage we find that:  

• "In 2015, David Poeppel, a neuroscientist at New York University and the Max Planck Institute, led a study to determine the acoustic qualities that differentiate fearful screams from other nonverbal vocalizations."

Thus from the above line, it is clear that the aim of the study was to determine the acoustic qualities that differentiate fearful screams making it the correct answer.

The correct answer is To see how the screams affected neural activity.  

Key Points

Reading the passage we come across the following line: 

• 'Poeppel also imaged the brains of his volunteers as they listened to screams to see how these sounds affected neural activity.'
• From this line, it is very evident that Poeppel imaged the brain to see how sounds affected neural activity.

Thus making it the correct answer.

The correct answer is Fearful screams and non-verbal vocalizations are the same. 

Key Points

Reading the passage we find that: 

• 'Though we're pretty good at recognizing a scream when we hear one, the wide variety of screams makes it difficult to pin down what defines them.'
• Thus it is clear that humans are good at recognizing a scream.
• 'Most people would say that the defining characteristic of a scream is that it is a focused loud and high-pitched,'
• Thus the given line is mentioned in the passage and is true.
• 'T**o do this, Poeppel and his colleagues compiled a corpus of screams lifted from YouTube videos and ones recorded in their lab, then asked volunteers to rank them according to how alarming the sound was.' 
• Thus the given line is mentioned in the passage and is true.
• 'Screaming is exhibited by many animals, but no species uses this extreme vocalization in as many different contexts as humans.'
• Thus the given line is mentioned and is true.
• 'David Poeppel, a neuroscientist at New York University and the Max Planck Institute, led a study to determine the acoustic qualities that differentiate fearful screams from other nonverbal vocalizations.'
• From the given line it is clear that fearful screams and non-verbal vocalizations are different and the given statement in the options is false.

Thus option 3 is false and therefore, is the correct answer.

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ (3/5) × (18/15) ÷ (9/5) + 60% of 20 = ?

⇒ (3/5) × (18/15) × (5/9) + 12 = ?

⇒ 2/5 + 12 = ?

⇒ (60 + 2)/5 = ?

⇒ 62/5 = ?

∴ The required answer is 62/5

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

152 + 112 – 182 + 63 = ?

⇒ 225 + 121 – 324 + 216 = ?

⇒ 562 - 324 = ?

⇒ ? = 238

∴ The required answer is 238

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ 30% of 50 + 16.66% × 48 – 20 + 13% of 200 = ?

⇒ 15 + 16.66% × 48 – 20 + 26 = ?

⇒ 15 + (1/6) × 48 – 20 + 26 = ?   (16.66% = 1/6)

⇒ 15 + 8 – 20 + 26 = ?

⇒ 23 – 20 + 26 = ?

⇒ 29 = ?

∴ The required answer is 29

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ [(20/7) × 63] ÷ (18) + (20/3) = ?

⇒ [(20 × 9] ÷ (18) + (20/3) = ?

⇒ [180] ÷ (18) + (20/3) = ?

⇒ 10 + (20/3) = ?

⇒ (30 + 20)/3 = ?

⇒ (50)/3 = ?

∴ The required answer is 50/3

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

⇒ 78 + 85 – 30% of 200 + (8 × 5) = ?

⇒ 78 + 85 – 60 + (8 × 5) = ?

⇒ 78 + 85 – 60 + (40) = ?

⇒ 78 + 25 + (40) = ?

⇒ 143 = ?

∴ The required answer is 143

Given:

(25 + 35) ÷ 4 × 15 - 644 ÷ 7 = ?

Concept Used: 

​

Calculation:

(25 + 35) ÷ 4 × 15 - 644 ÷ 7 = ?

⇒ 60 ÷ 4 × 15 - 92 = ?

⇒ ? = 225 - 92

⇒ ? = 133

∴ The value of (?) is 133.

Concept used:

Calculation:

⇒ [(252 – 63) × 3 – 2]1/2 = ?

⇒ [(625 – 216) × 3 – 2]1/2 = ?

⇒ [(409) × 3 – 2]1/2 = ?

⇒ [1227 – 2]1/2 = ?

⇒ [1225]1/2 = ?

⇒ 35 = ?

∴ The required answer is 35

Note: 

If the root is already in a number then only positive number is possible when we take square root.

Given:

15 × 18 + 20% of 45 = 9 × ?

Concept Used: 

​

Calculation:

15 × 18 + 20% of 45 = 9 × ?

⇒ 270 + 9 = 9 × ?

⇒ ? = 279/9

⇒ ? = 31

∴ The value of (?) is 31.

Given:

841 ÷ 29 + 650 ÷ 5 + ? = 35% of 1600

Concept Used: 

​

Calculation:

841 ÷ 29 + 650 ÷ 5 + ? = 35% of 1600

⇒ 29 + 130 + ? = 560

⇒ ? = 560 - 159

⇒ ? = 401

∴ The value of (?) is 401.

Given:

208 ÷ 13 × √441 + (13)2 = ?

Concept Used: 

​

Calculation:

208 ÷ 13 × √441 + (13)2 = ?

⇒ 16 × 21 + 169 = ?

⇒ ? = 336 + 169

⇒ ? = 505

∴ The value of (?) is 505.

Formula Used:

Number of Occupied floors = Total Number of floors - Number of Vacant Floors 

Calculation:

The ratio of the Number of occupied floors in building B to E

= 1120 : 840 ⇒ 4 : 3

∴ The ratio between the number of occupied floors in building B and that of building E is 4 : 3

Formula Used:

Number of Occupied floors = Total Number of floors - Number of Vacant Floors 

Calculation:

The number of occupied floors in building C is % less than the number of vacant floors in building E = (360 - 280)/360 × 100 ⇒ 22.22%

∴ The required percentage (approx) is 22%

Formula Used:

Number of Occupied floors = Total Number of floors - Number of Vacant Floors 

Calculation:

The total number of occupied floors of buildings B and C together = 1120 + 280 ⇒ 1400

The total number of occupied floors of building D and E together = 600 + 840 ⇒ 1440

The difference between (D + E) - (B + C) = 1440 - 1400 ⇒ 40

∴ The difference between the total number of occupied floors of buildings B and C together and that of buildings D and E together is 40

Formula Used:

Number of Occupied floors = Total Number of floors - Number of Vacant Floors 

Calculation:

Total number of people living on Building A = 600 × 3 ⇒ 1800

Total number of people living on Building D = 600 × 2 ⇒ 1200

Total number of people living on Building A and D = 1200 + 1800 ⇒ 3000 

∴ The total number of persons living in these 2 buildings is 3000

Formula Used:

Number of Occupied floors = Total Number of floors - Number of Vacant Floors 

Calculation:

The total number of occupied floors in all 5 buildings = 600 + 1120 + 280 + 600 + 840 ⇒ 3440

The average of the total number of occupied floors in all the 5 buildings.= 3440/5 ⇒ 688

∴ The average is 688

Calculation:

Here the pattern follows

⇒ 50 × 4 = 200

⇒ 200 × 3.5 = 700 

⇒ 700 × 3 = 2100

⇒ 2100 × 2.5 = 5250

∴ The required number is 5250

Calculation:

Here the pattern follows

⇒ 5 × 3 + 1 = 16

⇒ 16 × 4 + 1 = 65 

⇒ 65 × 5 + 1 = 326

⇒ 326 × 6 + 1 = 1957

∴ The required number is 1957

Calculation:

Here the pattern follows as

⇒ 20 + 3² = 29

⇒ 29 - 5² = 4

⇒ 4 + 7² = 53

⇒ 53  - 9² = -28

⇒ -28 + 11² = 93

∴ The required number is 93

Calculation:

Here the prime number addition pattern follows

⇒ 10 + 2 = 12

⇒ 12 + 3 = 15

⇒ 15 + 5 = 20

⇒ 20 + 7 = 27

⇒ 27 + 11 = 38

⇒ 38 + 13 = 51

∴ The required number is 51

Calculation:

Here the pattern follows as

⇒ 49 - 8 = 41

⇒ 41 - 8 = 33

⇒ 33 - 8 = 25

⇒ 25 - 8 = 17

⇒ 17 - 8 = 9

∴ The required number is 9

Shortcut Trick

Ratio of Prakash : Sohan = 5 : 3

3 units = 27 years ⇒ 1 unit = 9 years

Prakash's present age = 5 units = 5 × 9 = 45 years

Prakash's age after 3 years = 45 + 3 = 48 years

∴ The correct answer is 48 years.

Alternate Method

Given:

Present age of Sohan = 27 years

Ratio of Prakash and Sohan = 5 : 3

Calculations:

⇒ Let the present ages be 5x and 3x.

⇒ 3x = 27

⇒ x = 27 ÷ 3 = 9

⇒ Present age of Prakash = 5x = 5 × 9 = 45 years

⇒ Age of Prakash after 3 years = 45 + 3 = 48 years

∴ The correct answer is 48 years.

Additional Information

Ratio and Proportion in Ages

If the ratio of ages is a : b, and the actual age of one is known, the other can be found by multiplying the known value by the ratio fraction.

Future Age Calculation

To find the age after 'n' years, always add 'n' to the current present age. Age after n years = Present Age + n.

Shortcut Trick

Ratio of Profit (A : B) = (9900 − 4400) : 4400 = 5500 : 4400 = 5 : 4.

Profit Ratio = (Investment_A × Time_A) : (Investment_B × Time_B).

5 : 4 = (4500 × 12) : (4800 × t).

5 ÷ 4 = 54000 ÷ 4800t ⇒ t = (54000 × 4) ÷ (4800 × 5) = 9 months.

B joined after = 12 − 9 = 3 months.

∴ The correct answer is 3 months.

Alternate Method

Given: A investment = Rs. 4500, B investment = Rs. 4800, Total Profit = Rs. 9900, B profit = Rs. 4400.

Formulas: Profit Ratio = (I₁ × T₁) : (I₂ × T₂) | A profit = Total profit − B profit.

⇒ Profit of A = 9900 − 4400 = Rs. 5500.

⇒ (4500 × 12) ÷ (4800 × t) = 5500 ÷ 4400.

⇒ 54000 ÷ 4800t = 5 ÷ 4.

⇒ 4800t × 5 = 54000 × 4 ⇒ 24000t = 216000.

⇒ t = 216000 ÷ 24000 = 9 months.

⇒ B joined the business after = 12 − 9 = 3 months.

∴ The correct answer is 3 months.

Additional Information

Partnership Basics

In a partnership, the profit is distributed among partners in the ratio of the product of their investments and the time period for which the money was invested.

Time Calculation

Be careful to distinguish between the duration of investment (t) and the joining time (Total Time − t).

Shortcut Trick

Filling Pipe (A) = 12 hr, Emptying Pipe (B) = 20 hr (to empty 100%)

Net Efficiency = 1/12 − 1/20 = (5 − 3)/60 = 2/60 = 1/30

Time to fill full container = 30 hr

Time to fill 1/2 capacity = 30 ÷ 2 = 15 hr

∴ The correct answer is 15 hr.

Alternate Method

Given: Filling pipe (A) time = 12 hr. Emptying pipe (B) empties 50% in 10 hr ⇒ 100% in 20 hr.

Formula Used: Total Work = LCM of time | Efficiency = Total Work ÷ Time

⇒ Combined Efficiency of (A + B) = 5 − 3 = 2 units/hr

⇒ Target capacity to be filled = 1/2 × 60 = 30 units

⇒ Time required = Target Capacity ÷ Combined Efficiency

⇒ Time required = 30 ÷ 2 = 15 hr

∴ The correct answer is 15 hr.

Additional Information

Inlet and Outlet Pipes

Inlet pipes add water (positive efficiency) while outlet pipes remove water (negative efficiency).

Work and Wages

Wages are always distributed in the ratio of the work done or the ratio of efficiencies when time is constant.

Pipes and Cisterns Formula

If pipe A fills in x hours and pipe B empties in y hours, net work in 1 hour = (1/x − 1/y).

Shortcut Trick

Initial Ratio = 21 : 26 (Difference = 5)

New Ratio = 5 : 6 (Difference = 1)

Equalize difference: Multiply new ratio by 5 → 25 : 30

Change in units = 25 − 21 = 4 units. Given 4 units = 8, so 1 unit = 2.

Original numbers = 21 × 2 = 42 and 26 × 2 = 52. Subtract 4: (42 − 4) : (52 − 4) = 38 : 48 = 19 : 24.

∴ The correct answer is 19 : 24.

Alternate Method

Given: Ratio of two numbers = 21 : 26. Adding 8 to both results in 5 : 6.

Formula: Ratio = (a + k) / (b + k) = c / d

⇒ Let the numbers be 21x and 26x.

⇒ (21x + 8) / (26x + 8) = 5 / 6

⇒ 6(21x + 8) = 5(26x + 8)

⇒ 126x + 48 = 130x + 40

⇒ 4x = 8 → x = 2

⇒ Original numbers are 21 × 2 = 42 and 26 × 2 = 52.

⇒ After subtracting 4: (42 − 4) = 38 and (52 − 4) = 48.

⇒ Required ratio = 38 : 48 = 19 : 24.

∴ The correct answer is 19 : 24.

Additional Information

Ratio Balance Method

When the same value is added or subtracted from both terms of a ratio, the difference between the terms should remain constant. Multiply ratios to equalize these differences.

Duplicate and Sub-duplicate Ratio

Duplicate ratio of a:b is a²:b² and sub-duplicate ratio is √a:√b.

Compound Ratio

For ratios a:b and c:d, the compound ratio is (a×c) : (b×d).

Shortcut Trick

Ratio of Time (Downstream : Upstream) = 5 : 7

Ratio of Speed (Downstream : Upstream) = 7 : 5 (Inverse of time)

Boat Speed (B) : Stream Speed (S) = (7 + 5)/2 : (7 − 5)/2 = 6 : 1

Given 1 unit (Stream Speed) = 3 km/h, so 6 units (Boat Speed) = 6 × 3 = 18 km/h.

∴ The correct answer is 18 km/h.

Alternate Method

Given:

Time downstream (t_d) = 5 hours

Time upstream (t_u) = 7 hours

Speed of the stream (v) = 3 km/h

Formula Used:

Distance = Speed × Time

Downstream Speed = u + v | Upstream Speed = u − v (where u = boat speed)

Calculations:

⇒ Let the speed of the boat in still water be u km/h.

⇒ Downstream speed = (u + 3) km/h

⇒ Upstream speed = (u − 3) km/h

⇒ Distance is constant: (u + 3) × 5 = (u − 3) × 7

⇒ 5u + 15 = 7u − 21

⇒ 7u − 5u = 15 + 21

⇒ 2u = 36

⇒ u = 18 km/h

∴ The correct answer is 18 km/h.

Additional Information

Boat and Stream Basic Relations

Boat Speed in Still Water (u) = (Downstream Speed + Upstream Speed) ÷ 2

Stream Speed Relation

Stream Speed (v) = (Downstream Speed − Upstream Speed) ÷ 2

Average Speed for Round Trip

Average Speed = (Downstream Speed × Upstream Speed) ÷ Boat Speed in still water

Calculation:

Number of group X students in class A = (1/3) of 120 = 40

Number of students in group Y and group Z of class A = 120 - 40 = 80

Now, number of group Y sudents in class A = (3/4) × 80 = 60

Number of group Z sudents in class A = 80 - 60 = 20

Now, number of group X students in class B = (3/4) × 40 = 30

Number of group Y students in class B = 40 - 30 = 10

Now, Total number of students in class B = 250% of 40 = 100

Number of students in class C = 80% of (120 + 100) = 176

Now, number of students in group X of class C = (3/11) × 176 = 48

Number of students in group Y of class C = (5/11) × 176 = 80

Number of students in group Z of class C = (3/11) × 176 = 48

Here, we have also given the above data in tabular form.

From the table total number of students in class C = 176

∴ The number of students in class C is 176

Calculation:

Number of group X students in class A = (1/3) of 120 = 40

Number of students in group Y and group Z of class A = 120 - 40 = 80

Now, number of group Y sudents in class A = (3/4) × 80 = 60

Number of group Z sudents in class A = 80 - 60 = 20

Now, number of group X students in class B = (3/4) × 40 = 30

Number of group Y students in class B = 40 - 30 = 10

Now, Total number of students in class B = 250% of 40 = 100

Number of students in class C = 80% of (120 + 100) = 176

Now, number of students in group X of class C = (3/11) × 176 = 48

Number of students in group Y of class C = (5/11) × 176 = 80

Number of students in group Z of class C = (3/11) × 176 = 48

Here, we have also given the above data in tabular form.

Number of students in class A = 120

Number of students in class B = 100

The required % = (120/100) × 100 ⇒ 120%

∴ The number of students in class A is 120% of the number of students in class B

Calculation:

Number of group X students in class A = (1/3) of 120 = 40

Number of students in group Y and group Z of class A = 120 - 40 = 80

Now, number of group Y sudents in class A = (3/4) × 80 = 60

Number of group Z sudents in class A = 80 - 60 = 20

Now, number of group X students in class B = (3/4) × 40 = 30

Number of group Y students in class B = 40 - 30 = 10

Now, Total number of students in class B = 250% of 40 = 100

Number of students in class C = 80% of (120 + 100) = 176

Now, number of students in group X of class C = (3/11) × 176 = 48

Number of students in group Y of class C = (5/11) × 176 = 80

Number of students in group Z of class C = (3/11) × 176 = 48

Here, we have also given the above data in tabular form.

Total number of students in X = 40 + 30 + 48 ⇒ 118

∴ The total number of students of group X is 118

Calculation:

Number of group X students in class A = (1/3) of 120 = 40

Number of students in group Y and group Z of class A = 120 - 40 = 80

Now, number of group Y sudents in class A = (3/4) × 80 = 60

Number of group Z sudents in class A = 80 - 60 = 20

Now, number of group X students in class B = (3/4) × 40 = 30

Number of group Y students in class B = 40 - 30 = 10

Now, Total number of students in class B = 250% of 40 = 100

Number of students in class C = 80% of (120 + 100) = 176

Now, number of students in group X of class C = (3/11) × 176 = 48

Number of students in group Y of class C = (5/11) × 176 = 80

Number of students in group Z of class C = (3/11) × 176 = 48

Here, we have also given the above data in tabular form.

Number of students in group X in class B = 30

Number of students in a group Z in class B = 60

The required ratio = 30 : 60 ⇒ 1 : 2

∴ The ratio between group X and group Z students in class B is 1 : 2

Calculation:

Number of group X students in class A = (1/3) of 120 = 40

Number of students in group Y and group Z of class A = 120 - 40 = 80

Now, number of group Y sudents in class A = (3/4) × 80 = 60

Number of group Z sudents in class A = 80 - 60 = 20

Now, number of group X students in class B = (3/4) × 40 = 30

Number of group Y students in class B = 40 - 30 = 10

Now, Total number of students in class B = 250% of 40 = 100

Number of students in class C = 80% of (120 + 100) = 176

Now, number of students in group X of class C = (3/11) × 176 = 48

Number of students in group Y of class C = (5/11) × 176 = 80

Number of students in group Z of class C = (3/11) × 176 = 48

Here, we have also given the above data in tabular form.

Number of students in class A = 120

Number of students in class C = 176

Difference between  C & A = 176 - 120 = 56

∴ The difference between the number of students in class A and that of class C is 56

Shortcut Trick

Interest from Scheme A = 8000 × R% × 2 = 160R

Amount from Scheme A = 8000 + 160R

Interest from Scheme B = (8000 + 160R) × 12.5% × 1 = 1000 + 20R

Total Interest = 160R + 1000 + 20R = 3700

180R = 2700 ⇒ R = 15%

∴ The correct answer is 15%.

Alternate Method

Given: Principal (P₁) = ₹8000, Time (T₁) = 2 years, Rate (R₁) = R%, Rate (R₂) = 12.5%, Time (T₂) = 1 year, Total Interest = ₹3700.

Formula Used: Simple Interest (S.I.) = (P × R × T) ÷ 100; Amount (A) = P + S.I.

⇒ S.I.₁ = (8000 × R × 2) ÷ 100 = 160R

⇒ Amount₁ = 8000 + 160R

⇒ S.I.₂ = [(8000 + 160R) × 12.5 × 1] ÷ 100

⇒ S.I.₂ = (8000 + 160R) × 0.125 = 1000 + 20R

⇒ Total Interest = S.I.₁ + S.I.₂ = 3700

⇒ 160R + 1000 + 20R = 3700

⇒ 180R = 2700

⇒ R = 2700 ÷ 180 = 15

∴ The correct answer is 15%.

Additional Information

Simple Interest vs Amount

Simple Interest is calculated only on the principal amount, while Amount is the sum of Principal and Interest (A = P + S.I.).

Fractional Equivalent of Percentage

Converting 12.5% to a fraction (1/8) simplifies calculations significantly in competitive exams.

Successive Investment

When the Amount of one scheme is invested in another, the new principal becomes P₂ = P₁ × (1 + R₁T₁/100).

Shortcut Trick

Speed of Train A = 36 × (5/18) = 10 m/s. Length A = 10 × 20 = 200 m.

Length B = 200 + 100 = 300 m. Platform = 500 m.

Total Distance for B = 300 + 500 = 800 m. Speed B = 18 × (5/18) = 5 m/s.

Time taken by B = 800 ÷ 5 = 160 sec.

∴ The correct answer is 160 sec.

Alternate Method

Given: Speed of Train A = 36 km/hr, Time to cross pole = 20 sec, Length of Train B = Length A + 100 m, Speed of Train B = 18 km/hr, Platform length = 500 m.

Formula Used: Distance = Speed × Time; Time = Distance ÷ Speed; 1 km/hr = 5/18 m/s.

⇒ Speed of Train A in m/s = 36 × (5/18) = 10 m/s.

⇒ Length of Train A = Speed × Time = 10 × 20 = 200 m.

⇒ Length of Train B = 200 + 100 = 300 m.

⇒ Speed of Train B in m/s = 18 × (5/18) = 5 m/s.

⇒ Total Distance to be covered by B = Length of B + Length of Platform = 300 + 500 = 800 m.

⇒ Time taken by B = 800 ÷ 5 = 160 sec.

∴ The correct answer is 160 sec.

Additional Information

Unit Conversion

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

Train Crossing Concepts

When a train crosses a pole or stationary person, distance = length of train. When it crosses a platform or bridge, distance = length of train + length of platform.

Relative Speed

If two trains move in the same direction, relative speed = S₁ − S₂. If they move in opposite directions, relative speed = S₁ + S₂.

Shortcut Trick

Initial Ratio (Alcohol : Water) = 11 : 6 (Total units = 17)

Final Ratio (Alcohol : Water) = 5 : 3

Equate Alcohol: multiply initial by 5 and final by 11 → New Ratios: 55 : 30 and 55 : 33.

Total initial 85 units = 85 litres ⇒ 1 unit = 1 litre.

Water added = 33 − 30 = 3 units = 3 litres.

∴ The correct answer is 3 litres.

Alternate Method

Given: Total volume = 85 litres, Initial ratio = 11 : 6, Final ratio = 5 : 3.

Formula: Value of one part = Total Volume ÷ Sum of ratio parts.

⇒ Initial Alcohol = (11/17) × 85 = 55 litres.

⇒ Initial Water = (6/17) × 85 = 30 litres.

⇒ Let x litres of water be added.

⇒ New Alcohol / New Water = 55 / (30 + x) = 5 / 3.

⇒ 165 = 5 × (30 + x)

⇒ 165 = 150 + 5x

⇒ 5x = 15 ⇒ x = 3 litres.

∴ The correct answer is 3 litres.

Additional Information

Constant Quantity Concept

When only one component (e.g., water) is added to a mixture, the quantity of the other component (e.g., alcohol) remains constant. Equating the constant part in both ratios simplifies calculations.

Alligation Method

Can be used by taking water concentration. Initial water (6/17) and added pure water (1/1) are mixed to get a final concentration of 3/8.

Replacement vs Addition

In addition, total volume increases. In replacement, a portion of the mixture is removed and the same volume of a component is added, keeping total volume constant.

Shortcut Trick

Let Cost Price (CP) be 100%.

Marked Price (MP) = 100% + 25% = 125%.

Selling Price (SP) = 125% × (100 − 12)% ÷ 100 = 125% × 0.88 = 110%.

Profit% = SP − CP = 110% − 100% = 10%.

Given, 10% = Rs. 55. ∴ 100% = Rs. 550.

∴ The correct answer is Rs 550.

Alternate Method

Given: Markup = 25%, Discount = 12%, Profit = Rs. 55.

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

⇒ Let Cost Price = x.

⇒ Marked Price = x + 0.25x = 1.25x.

⇒ Selling Price = 1.25x − (12% of 1.25x) = 1.25x − 0.15x = 1.10x.

⇒ Profit = 1.10x − x = 0.10x.

⇒ 0.10x = 55 ⇒ x = 55 ÷ 0.10 = 550.

∴ The correct answer is Rs 550.

Additional Information

Successive Percentage Method

Net Profit% can be calculated using a + b + (a × b) ÷ 100, where a is markup% and b is discount% (negative).

Relation between CP and MP

The ratio of CP to MP is given by: CP ÷ MP = (100 − Discount%) ÷ (100 + Profit%).

Shortcut Trick

Percentage difference between the two cases = 40% − 25% = 15%.

Marks difference between failing by 64 and passing by 32 = 64 + 32 = 96 marks.

15% of Maximum Marks = 96.

100% = (96 ÷ 15) × 100 = 6.4 × 100 = 640.

∴ The correct answer is 640 marks.

Alternate Method

Given:

Case 1: Marks = 25% of Maximum Marks, Result = Pass Marks − 64

Case 2: Marks = 40% of Maximum Marks, Result = Pass Marks + 32

Calculations:

⇒ Let the Maximum Marks be M.

⇒ 0.25 × M + 64 = Pass Marks

⇒ 0.40 × M − 32 = Pass Marks

⇒ 0.40 × M − 32 = 0.25 × M + 64

⇒ 0.40M − 0.25M = 64 + 32

⇒ 0.15M = 96

⇒ M = 96 ÷ 0.15

⇒ M = 640

∴ The correct answer is 640 marks.

Additional Information

Pass Percentage Formula

Pass % = (Marks Obtained + Marks needed to pass) ÷ Maximum Marks × 100.

Percentage Difference Rule

When comparing two scenarios of pass/fail, the difference in percentages is always equal to the sum of (failed by marks + passed by more marks).

Base Value in Percentages

The Maximum Marks always represent the 100% base value in examination-based percentage problems.

1) D is second to the right of F. 

2) Two people sit between C and D.

3) Three people sit between G and A.

4) G is not an immediate neighbor of D. 

5) Two people sit between H and B.

6) H is an immediate neighbor of E.  (This eliminates the case 2) 

Hence, H is facing C.

1) D is second to the right of F. 

2) Two people sit between C and D.

3) Three people sit between G and A.

4) G is not an immediate neighbor of D. 

5) Two people sit between H and B.

6) H is an immediate neighbor of E.  (This eliminates the case 2) 

Hence, D is second to second to the left of E.

1) D is second to the right of F. 

2) Two people sit between C and D.

3) Three people sit between G and A.

4) G is not an immediate neighbor of D. 

5) Two people sit between H and B.

6) H is an immediate neighbor of E.  (This eliminates the case 2) 

Hence, both B and F are immediate neighbor of C.

1) D is second to the right of F. 

2) Two people sit between C and D.

3) Three people sit between G and A.

4) G is not an immediate neighbor of D. 

5) Two people sit between H and B.

6) H is an immediate neighbor of E.  (This eliminates the case 2) 

Hence, H is an immediate neighbor of D is true.

1) D is second to the right of F. 

2) Two people sit between C and D.

3) Three people sit between G and A.

4) G is not an immediate neighbor of D. 

5) Two people sit between H and B.

6) H is an immediate neighbor of E.  (This eliminates the case 2) 

All the given pairs are opposite to each other except F - H. 

Hence, "F - H" is odd one out.

Minimum possible venn diagram

I. Some words are not sentences. → True (Only a few words are sentences. Means some words are sentences and some words are not sentences) 

II. Some vowels are sentences. → False (This is possible but not definite) 

Hence, Only conclusion I follows.

Minimum possible venn diagram 

I. No prime is number. → False (It is definitely false) 

II. Some prime are natural. → True (numbers which are prime are definitely natural) 

Hence, Only conclusion II follows.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some cups are not bucket. → True (It is clearly mentioned in statement that only few cups are buckets that means some cups are definitely not bucket)

II. Some cups are not jug. → True (Part of cups which is bucket is definitely not jug)

Hence, both I and II follows.

1. Two people sit between E and C.

2. E sits at one of the extreme ends.

3. A sits second to the right of C.

4. B sits fourth to the left of F.

5. F is not an immediate neighbor of C. (This eliminates case 2)

6. H sits third to the left of D.

7. D does not sit at extreme ends.

Hence, ‘G’ sits immediately to the right of F.

1. Two people sit between E and C.

2. E sits at one of the extreme ends.

3. A sits second to the right of C.

4. B sits fourth to the left of F.

5. F is not an immediate neighbor of C. (This eliminates case 2)

6. H sits third to the left of D.

7. D does not sit at extreme ends.

Hence, no one sits between C and B.

1. Two people sit between E and C.

2. E sits at one of the extreme ends.

3. A sits second to the right of C.

4. B sits fourth to the left of F.

5. F is not an immediate neighbour of C. (This eliminates case 2)

6. H sits third to the left of D.

7. D does not sit at extreme ends.

After rearrangement: 

All of them change their position as compared to their original seating position.

Hence, none unchanged as compared to their original seating position.

1. Two people sit between E and C.

2. E sits at one of the extreme ends.

3. A sits second to the right of C.

4. B sits fourth to the left of F.

5. F is not an immediate neighbor of C. (This eliminates case 2)

6. H sits third to the left of D.

7. D does not sit at extreme ends.

E → First from the left end, G → First from the right end

B → Third from the left end, A → Third from the right end

D → Fifth from the left end, C → Fifth from the right end

F → seventh from the left end, H → seventh from the right end

A → Sixth from the left end, F→ Second from the right end

Hence, ‘A - F’ does not belong to the group.

1. Two people sit between E and C.

2. E sits at one of the extreme ends.

3. A sits second to the right of C.

4. B sits fourth to the left of F.

5. F is not an immediate neighbor of C. (This eliminates case 2)

6. H sits third to the left of D.

7. D does not sit at extreme ends.

Hence, H sits second from the left end.

Hence, H is 16 m in the East direction with respect to A.

Hence, E is in South East direction with respect to C.

Forward Pair - CI

Backward Pair - ON, ON

Hence, Three such pairs each of which has as many letters between them in the word as they have between them in the English alphabetical series.

1) Two persons buy items between B and A

2. A buys an item after B.

3) A buys item immediately before G and after C. 

4) Three-person buys items between A and D. 

5. Two people buy item between H and C. (This eliminates case 4)

6. F buys an item before E.

7. Neither F nor E buys items first or last. (This eliminates case 2 and case 3)

Hence two person buys F and G.

1) Two persons buy items between B and A

2. A buys an item after B.

3) A buys item immediately before G and after C. 

4) Three-person buys items between A and D. 

5. Two people buy item between H and C. (This eliminates case 4)

6. F buys an item before E.

7. Neither F nor E buys items first or last. (This eliminates case 2 and case 3)

Hence, D buys the the item at last.

1) Two persons buy items between B and A

2. A buys an item after B.

3) A buys item immediately before G and after C. 

4) Three-person buys items between A and D. 

5. Two people buy item between H and C. (This eliminates case 4)

6. F buys an item before E.

7. Neither F nor E buys items first or last. (This eliminates case 2 and case 3)