SBI Clerk Prelims Memory Based Paper (Held On: 11 Jul 2021 Shift 1) (Previous Year Paper)

The correct answer is Option 2.

 

• The error is in part B of the sentence.
• A singular verb is used after One of, Neither of, Either of, and Each of.
• Eg. Either Shradha or Sujata is going to be a winner.
• Hence we need to replace 'are' with 'is'

Correct sentence - One of my best friends is planning to start a new venture.

 

• The Noun is Part of the sentence which defines persons, Place or things.
• Helping verbs in the sentence are decided with the help of a noun or subject.

The correct answer is '(A)'.

Key Points

Reading the sentence we find that:

• The plural linking verb is used in part A is incorrect as there is a subject-verb disagreement.
• Clergy ( the entire class of religious officials) is a collective Noun which follows the verb in singular form
• The sentence can be made correct if we use the Singular linking verb is.

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The correct sentence will be: Neither the Pope nor the clergy is responsible for the actions taken in the name of religion in the country.

Additional Information

• Sometimes two subjects are joined by ‘nor’ and are of different count
• Then the succeeding verb agrees in count with the one nearest to it.
• So, in the given sentence, the succeeding verb is singular as clergy is singular.

The correct answer is '(B)'.

Key Points

Reading the sentence we find that:

• The conjunction than used in part B is incorrect.
• We need to use the word to after the superlative adjective superior for the sentence to be correct.

The correct sentence will be:Can the French be so enormously superior to us that we could not beat them?

Additional Information

• A Comparative Adjective is a word that describes a noun by comparing it to another noun.
• They are followed by the word ‘than’.
• A Superlative Adjective is a word that describes a noun by comparing it to two or more nouns to the highest or lowest degree.
• They are followed by the word ‘to’.

The correct answer is '(C)'.

Key Points

Reading the sentence we find that:

• The pronoun their used in part C is incorrect.
• Their  is used to reflect possession. It means that something 'belongs' to someone.
• The sentence can be made correct if we use the pronoun there.

The correct sentence will be: The sun had been under the cloud all day, and there had been brief showers.

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 '(C)'.

Key Points

Reading the sentence we find that:

• The adjective alone used in part C has been placed incorrectly.
• Alone is an adjective that cannot be placed before the linking verb lived.
• So the adjective needs to be placed after the noun, and the sentence should be accordingly restructured for it to be correct.

The correct sentence will be: For four years and four months he lived alone on the island without any human contact.  

Additional Information

• Generally adjectives are placed before nouns.
• But some adjectives can only be placed after the noun or linking verbs.
• These include - alike, alight, alive, fine, glad, ill, poorly, alone, ashamed, awake, aware and unwell.
  - the sisters were very much alike
  - he looked poorly

The correct answer is '(B)'.

Key Points

Reading the sentence we find that:

• The preposition in used in part B is incorrect.
• The adjective grateful (feeling or showing an appreciation for something done or received.) is always followed by the preposition to when it is required.

The correct sentence will be: I would be grateful to hear from anyone who may be able to help.

Additional Information

• Certain verbs, nouns, adjective and participles are followed by particular prepositions only.
• abounds (verb) followed by preposition in.
• attend (verb) followed by preposition to.
• grateful (adjective) followed by preposition to.

The correct answer is Culture.

Key Points

Culture: the ideas, customs, and social behaviour of a particular group of people or society

The line refers to Japan not being considered to have a predominant sports tradition by other countries around the world.

Additional Information

The correct answer is Perceptions. 

Key Points

Perceptions: the ways in which something is regarded, understood, or interpreted

The given line talks about other countries having interpretations of their own regarding Japan's history, tradition and culture.

Additional Information

The correct answer is Development. 

Key Points

Development: a specified state of growth or advancement

The context talks about Japan's association with sports-  as viewed by other counties. The given line talks about various facets of Japan, one of them being its technological advancements.

Additional Information

The correct answer is Equipment. 

Key Points

Equipment: the necessary items for a particular purpose

The line talks about students carrying a specialized sports item- Kyodo- while coming home from school. 

Additional Information

 

The word equipment has no plural form.

The correct answer is Understand. 

Key Points

Understand: perceive the intended meaning of (words, a language, or a speaker)

The given line talks about the need for looking into the religious and historical background of Japan to perceive its position in sports. 

Additional Information

The correct answer is A. 

Key Points

The word suit is incorrectly spelt as siut.  

• Suit: a set of outer clothes made of the same fabric and designed to be worn together, typically consisting of a jacket and trousers or a jacket and skirt.

Therefore the error lies in part A.

• Armour: clothing, often made of metal, that soldiers wore in earlier times to protect themselves (धातु का बना आवरण जो प्राचीन समय में सैनिक आत्मरक्षा के लिए पहनते थे; कवच, बख्‍़तर)
• Excellent: very good; of high quality (बहुत बढ़िया; उच्‍च स्‍तर का, उत्‍कृष्‍ट)
• Protection: the act of keeping somebody/something safe so that he/she/it is not harmed or damaged (सुरक्षा, हिफ़ाज़त)
• Hence, the given answer is correct.

The correct answer is C. 

Key Points

• The word is incorrectly spelt as attendence.
• The correct spelling is attendance.

Important Points

• Let us look at the other emboldened words:
• Gotten: (it is the past participle of 'got') to receive, obtain or buy something. (किसी वस्‍तु को पाना, लेना या ख़रीदना)
• Promotion: a move to a higher position or more important job (पदोन्‍नति या अधिक बड़ी नौकरी की प्राप्ति)
• Enough: as much or as many of something as necessary (पर्याप्त, काफ़ी, जितना (मात्रा या संख्‍या) आवश्‍यक हो उतना)
• Hence, the given answer is correct.

The correct answer is A. 

Key Points

• The word view is incorrectly spelt as veiw.
• View means an opinion or a particular way of thinking about something; the ability to see something or to be seen from a particular place.
• All other words in bold have correct spellings.
• Hence, the given answer is correct.

The correct answer is C. 

Key Points

• The word cereal is incorrectly spelt as cerial.
• Cereal: a breakfast food made from roasted grain, typically eaten with milk.
• Bought: (past tense: bought; past participle: bought)  to get something by paying money for it
• favourite: liked more than any other
• forgot: (past tense: forgot) to not be able to remember something

The correct answer is B. 

Key Points

• The word dramatically is wrongly spelt as drammatically.
• Let us look at the other emboldened words:
• Improved: to become or to make something better. (किसी स्थिति का बेहतर होना या उसे बेहतर बनाना, सुधरना या सुधारना)
• Lead: to go with or in front of a person or animal to show the way or to make him/her/it go in the right direction. (किसी व्‍यक्ति या पशु को साथ ले जाना या उसे रास्‍ता दिखाना या सही दिशा में भेजना)
• Left: to leave (छोड़ देना)

The correct answer is Option 2)i.e. I have another. 

Key Points

• In the given sentence, the subject ‘I’ have already introduced my brother ‘Oliver’ and now we are talking about a different brother.
• The use of ‘other’ is incorrect before ‘brother.’❌
• The most appropriate determiner for the given sentence is ‘another’.✔️
• When we use the indefinite article ‘an’ before other, we write it as one word another. ‘Another’ means ‘one more, an additional, extra, an alternative or different’.
• Example: Is there another cafe around here we could go to? (alternative or different)
• We use another with singular nouns.
• Here, in the given sentence ‘brother’ is a singular noun.
• Therefore, by reading the above explanation we find that option 2 is correct.

📌Correct sentence: You’ve met Oliver, but I have another brother whom you haven’t met, called Lucas.✔️

Additional Information 

• Another is singular. We don’t use it with plural nouns.
• Example: Another interesting places to visit include the old harbor and the castle.❌(Incorrect)
• Example: Other interesting places to visit include the old harbor and the castle.✔️(Correct)
• We write another as one word.
• Example: There is an other car park a little further down the same street.❌ (Incorrect)
• Example: There is another car park a little further down the same street.✔️ (Correct)
• The words another and other mean the same thing, except that another is used with a singular noun and other is used with uncountable and plural nouns.

Correct option - 5

The above-mentioned sentence is error free and does not require any corrections.

Therefore, the correct answer is option 5, i.e., No corrections required.

The correct answer is Option 4 i.e. 'Going to meet'

Explanation: The phrase 'going to a meeting' is grammatically incorrect and therefore needs to be corrected. By reading the above-mentioned sentence.

Nevertheless is an adverb which means 'that contrasts' before is a preposition hence we need a prepositional object and it can be a noun/gerund/pronoun and hence in this case we will use a gerund form. The action of 'meeting' hasn't performed yet hence use an infinitive not a preposition after the gerund. So 'to meet' is correct.

Additional Information

The meaning of mien is 'a person's appearance or manner.'

So the correct sentence is:

Nevertheless, before going to meet Samuel, she assumed a calm and dignified mien.

Correct option - 2

The phrase 'unaffected by simple' does not fit into the sentence grammatically and therefore needs to be corrected. The sentence suggests that 'his conversation was without being affected simple and frank...'

Option 1 and option 4 are grammatically incorrect and therefore cannot be used.

The phrase 'unaffected and simple and frank' also does not make any sense and therefore option 3 is also rejected.

This leaves us with option 2, i.e., 'Unaffectedly simple', to be the only correct answer.

Correct sentence: His conversation was unaffectedly simple and frank; his language natural; always abounding in curious anecdotes.

The correct answer is Option 2 i.e. 'had been talking'

Explanation: Firstly, the verb ‘has’ does not agree with the noun ‘roommates’ in number. It is correct to say ‘roommates have’.

Second, the action of talking completed before they went to bed. Since the action of ‘going to bed’ is in simple past, its preceding action here must be in past perfect continuous tense ‘had been talking’ and NOT in present perfect continuous tense ‘have been talking’

So the Correct sentence is

The two roommates had been talking all night and later on, they went to bed in the morning.

The correct answer is: The culture where the language belongs must be referenced.  

Key Points

Reading the passage we find that: 

• '*When learning or teaching a language, *the culture where the language belongs must be referenced because language is very much ingrained in the culture.**'

Thus from the given point, it is clear that the correct answer is The culture where the language belongs must be referenced.

The correct answer is Body Language. 

Key Points

Reading the passage we find that: 

• "*Body language, which is also known as kinesics, is the *most obvious type of paralanguage.**"
• Thus it is clear that the most obvious type of paralanguage is body language.

Therefore the correct answer is Body Language.

The correct answer is Both 1 and 3.

Key Points

Reading the passage we find that: 

• 'These specific communication techniques of one culture are learned mostly by imitating and observing people, initially from parents and immediate relatives and later from friends and people outside the close family circle.'
• Here we find that communication techniques of once culture are learned mostly by first imitating and observing people initially parents and which form the close family circle and then friends and people outside the close family circle.

Thus we can conclude that both 1 and 3 mentioned in the options is the correct answer.

The correct answer is When you grow up in a society you ignore glances, gestures and little changes in voice. 

Key Points

Reading the passage we find that: 

• "When you grow up in a specific society, it is inevitable that you learn the glances, gestures and little changes in voice or tone and other communication tools to emphasize or alter what you want to do or say."
• From this line, it is clear that the sentence given in the option is false whereas all the other given options are mentioned in the passage.

Therefore the correct answer is: When you grow up in a society you ignore glances, gestures and little changes in voice.

The correct answer is None of the above. 

Key Points

Reading the passage we find the following line: 

• 'Alfred L Krober, a cultural anthropologist from the United States said that culture started when speech was available, and from that beginning, the enrichment of either one led the other to develop further.'
• Looking at the options we find that this point is not reflected in any of the options.

Therefore the correct answer is None of the above.

The correct answer is Messages exchanged with one another using a given language. 

Key Points

Reading the passage we find that:  

'Ferruccio Rossi-Landi, a philosopher from Italy whose work focused on philosophy, semiotics and linguistics said that a speech community is made up of all the messages that were exchanged with one another using a given language,'

Thus from the given point it is clear that the correct answer is Messages exchanged with one another using a given language.

The correct answer is The development of their cognitive abilities. 

Key Points

Reading the given sentence we find that: 

• 'Rossi-Landi further added that young children learn their language and culture from the society they were born in. In the process of learning, they develop their cognitive abilities as well.'
• Thus here it is mentioned that they develop their cognitive abilities as well.

Therefore we can conclude that the correct answer is The development of their cognitive abilities.

The correct answer is Intricate. 

Key Points

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

• Complex: consisting of many different and connected parts.
• Intricate: Very complicated or detailed.

Thus it is clear that intricate is the synonym of complex. 

Additional Information 

 

Lucid: Easy to understand.

The correct answer is Avoidable. 

Key Points

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

• Inevitable: certain to happen; unavoidable.
• Avoidable: Able to avoided.

Thus from the given meanings, it is clear that the correct answer is Avoidable as both words have the opposite meaning. 

Additional Information

• Coarse: Rough or harsh in texture.
• Inescapable: unable to be avoided or denied.
• Splendid: Very impressive; magnificent.

Given:

40% of 60 + 16.66% × 54 – 20 + 13 = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

40% of 60 + 16.66% × 54 – 20 + 13 = ?

⇒ 40/100 × 60 + 1/6 × 54 – 20 + 13 = ?

⇒ ? = 24 + 9 - 20 + 13

? = 26

∴ The value of ? is 26

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

25 + 41 × (28 ÷ 7) – 132 = ?

⇒ 25 + 41 × 4 - 169 = ?

⇒ ? = 25 + 164 - 169

⇒ ? = 20

∴ The value of ? is 20

Given:

[(61/13) × 91] ÷ 7 + 9 – 25 = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

[(61/13) × 91] ÷ 7 + 9 – 25 = ?

⇒ [61 × 7] ÷ 7 + 9 – 25 = ?

⇒ ? = 61 + 9 - 25

? = 45

∴ The value of ? is 45

Given:

(40 + 24) ÷ 8 × 18 – ? = 126

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

(40 + 24) ÷ 8 × 18 – ? = 126

⇒ (64) ÷ 8 × 18 – ? = 126

⇒ ? = 8 × 18 - 126

? = 18

∴ The value of ? is 18

Given:

(152 – 114) ÷ 3 – 40 + 23 = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

(152 – 114) ÷ 3 – 40 + 23 = ?

⇒ (225 - 114) ÷ 3 - 40 + 8 = ?

⇒ ? = 37 - 40 + 8

? = 5

∴ The value of ? is 5

Given:

(15 + 24) × 3 ÷ 13 + 18 – 5 = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

(15 + 24) × 3 ÷ 13 + 18 – 5 = ?

⇒ (39) × 3 ÷ 13 + 18 - 5 = ?

⇒ ? = 9 + 18 - 5

? = 22

∴ The value of ? is 22

Given:

78 + 85 – (13 × 8) + (81 ÷ 3) = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

78 + 85 – (13 × 8) + (81 ÷ 3) = ?

⇒ 163 - 104 + 27 = ?

⇒ ? = 190 - 104 

? = 86

∴ The value of ? is 86

Given:

48 × 7 ÷ 12 + 33 – 72 = √?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

48 × 7 ÷ 12 + 33 – 72 = √?

⇒ 28 + 27 – 49= √?

⇒ √? = 6 

? = 36

∴ The value of ? is 36

Given:

20 + 39 – 78 + (17 × 3) – 15 = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

20 + 39 – 78 + (17 × 3) – 15 = ?

⇒ 59 – 78 + 51 – 15 = ?

⇒ ? = 17 

? = 17

∴ The value of ? is 17

Given:

√(89 + 32) + 53 – (49 × 2) = ?

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

√(89 + 32) + 53 – (49 × 2) = ?

⇒ √(121) + 125 – 98 = ?

⇒ ? = 38

? = 38

∴ The value of ? is 38

Calculation:

number of fiction books sold from shop B = 175

number of comic books sold from shop D = 300

∴ Required difference = 300 - 175 = 125

Calculation:

number of fiction books sold from all the 5 shops = (350 + 175 + 250 + 200 + 350) = 1325

∴ Required average = 1325/5 = 265

Calculation:

Number of comic books sold from shop E = 275

number of comic books sold from shop A = 200

∴ Required % = (275 - 200)/200 × 100 = 37.5%

Calculation:

total books sold from shop C = (150 + 250) = 400

total books sold from shop B = (175 + 225) = 400

∴ Required ratio = 400 : 400 = 1 : 1

Calculation:

 

number of comic books sold from all the 5 shops = (200 + 225 + 150 + 300 + 275) = 1150

number of fiction books sold from all the 5 shops = (350 + 175 + 250 + 200 + 350) = 1325

∴ Required difference = (1325 - 1150) = 175

Given:

40, 20, 20, 30, 60, ?

Calculation:

The series follows the following pattern:

40 × 0.5 = 20

20 × 1 = 20

20 × 1.5 = 30

30 × 2 = 60

60 × 2.5 = 150

Given:

27, 32, 42, 57, 77, ?

Calculation:

The series follows the following pattern:

27 + (5 × 1) = 32

32 + (5 × 2) = 42

42 + (5 × 3) = 57

57 + (5 × 4) = 77

77 + (5 × 5) = 102

Given:

15, 31, 63, 127, ?, 511

Calculation:

The series follows the following pattern:

15 × 2 + 1 = 31

31 × 2 + 1 = 63

63 × 2 + 1 = 127

127 × 2 + 1 = 255

Calculation:

The series follows the following pattern:

⇒ 4 + 1³ = 5

⇒ 5 + 2³ = 13

⇒ 13 + 3³ = 40

⇒ 40 + 4³ = 104

⇒ 104 + 5³ = 229

∴ The value of ? is 229

Given:

7, 14, 42, 168, 840, ?

Calculation:

The series follows the following pattern:

7 × 2 = 14

14 × 3 = 42

42 × 4 = 168

168 × 5 = 840

840 × 6 = 5040

Shortcut Trick

Net change in marks = (64 + 84) − (54 + 74) = 148 − 128 = +20

Average change = Net change ÷ Total students = 20 ÷ 20 = +1

Correct Average = Old Average + Average change = 70 + 1 = 71

∴ The correct answer is 71.

Alternate Method

Given:

Number of students (n) = 20

Initial Average marks = 70

Incorrect marks = 54 and 74

Correct marks = 64 and 84

Calculations:

⇒ Total initial sum of marks = 20 × 70 = 1400

⇒ Sum of incorrect marks = 54 + 74 = 128

⇒ Sum of correct marks = 64 + 84 = 148

⇒ Correct total sum = 1400 − 128 + 148

⇒ Correct total sum = 1420

⇒ Correct average = Correct total sum ÷ Total students

⇒ Correct average = 1420 ÷ 20 = 71

∴ The correct answer is 71.

Additional Information

Net Deviation Method

Correct Average = Observed Average + (Sum of Correct Values − Sum of Incorrect Values) ÷ Total Number of Items.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

Age difference remains constant at 14 years regardless of time.

Ratio after 6 years = 17 : 24. Difference in ratio units = 24 − 17 = 7 units.

7 units = 14 years ⇒ 1 unit = 2 years.

Aditya's age after 6 years = 17 × 2 = 34 years.

Present age of Aditya = 34 − 6 = 28 years.

∴ The correct answer is 28 years.

Alternate Method

Given: Ratio of ages after 6 years = 17 : 24; Difference in ages = 14 years.

Let the ages of Aditya and Vaibhav after 6 years be 17x and 24x.

⇒ 24x − 17x = 14

⇒ 7x = 14

⇒ x = 2

⇒ Aditya's age after 6 years = 17 × 2 = 34 years

⇒ Aditya's present age = 34 − 6 = 28 years

∴ The correct answer is 28 years.

Additional Information

Concept of Age Difference

The difference between the ages of two persons never changes with time. If the difference is 14 years now, it will remain 14 years after n years or n years ago.

Ratio Scaling

When the ratio is a:b and the real difference is D, then 1 unit = D ÷ (b − a). Multiply this unit with the ratio parts to get the actual ages at that point in time.

Shortcut Trick

Length of Train B = Speed × Time = 10 × 40 = 400 m.

Length of Train A = 400 − 150 = 250 m.

Total Distance (A + Platform) = Speed of A × Time = 20 × 30 = 600 m.

Length of Platform = 600 − 250 = 350 m.

∴ The correct answer is 350 metres.

Alternate Method

Given: Speed of Train A = 20 m/s, Time to cross platform = 30 s. Speed of Train B = 10 m/s, Time to cross pole = 40 s. Length B = Length A + 150 m.

Formula Used: Distance = Speed × Time; When crossing a pole, Distance = Length of Train; When crossing a platform, Distance = Length of Train + Length of Platform.

⇒ Length of Train B (L_B) = Speed_B × Time_pole

⇒ L_B = 10 m/s × 40 s = 400 m.

⇒ Length of Train A (L_A) = L_B − 150 = 400 − 150 = 250 m.

⇒ For Train A crossing Platform: (L_A + L_P) = Speed_A × Time_platform

⇒ 250 + L_P = 20 × 30

⇒ 250 + L_P = 600

⇒ L_P = 600 − 250 = 350 m.

∴ The correct answer is 350 metres.

Additional Information

Relative Speed

When two trains move in the same direction, relative speed is (u − v). In opposite directions, it is (u + v).

Unit Conversion

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

Crossing Objects

When a train crosses a point object (pole, man), distance = length of train. When crossing a platform or bridge, distance = length of train + length of object.

Shortcut Trick

Net efficiency of (A + B) = 100% / 20 hr = 5% per hour.

Efficiency of C (emptying) = 40% / 20 hr = 2% per hour.

Combined efficiency of (A + B − C) = 5% − 2% = 3% per hour.

Time to fill 60% of the tank = 60% ÷ 3% = 20 hours.

∴ The correct answer is 20 hr.

Alternate Method

Given:

Time taken by (A + B) to fill the tank = 20 hours

Time taken by C to empty 40% of the tank = 20 hours

⇒ Time taken by C to empty the full tank (100%) = (20 ÷ 40) × 100 = 50 hours

Calculations:

⇒ Combined efficiency of (A + B + C) = 5 − 2 = 3 units/hour

⇒ 60% of Total Work = 0.60 × 100 = 60 units

⇒ Time taken = 60 units ÷ 3 units/hour

⇒ Time taken = 20 hours

∴ The correct answer is 20 hr.

Additional Information

Inlet and Outlet Pipes

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

Work Done Formula

Total Work = Efficiency × Time. For partial work, Required Time = (Fraction × Total Work) ÷ Net Efficiency.

Efficiency Percentage

Efficiency can be calculated as % of tank filled per unit time where 100% represents the full capacity.

Shortcut Trick

Downstream Speed = Upstream Speed + 2 × Stream Speed

Downstream Speed = 7 + 2 × 3 = 13 km/hr

Time Taken = Distance ÷ Downstream Speed = 91 ÷ 13 = 7 hr

∴ The correct answer is 7 hr.

Alternate Method

Given:

Stream Speed (v) = 3 km/hr

Upstream Speed (u) = 7 km/hr

Distance = 91 km

Formula Used:

Upstream Speed (u) = Boat Speed (b) − Stream Speed (v)

Downstream Speed (d) = Boat Speed (b) + Stream Speed (v)

Calculations:

⇒ 7 = b − 3

⇒ b = 7 + 3 = 10 km/hr (Speed of boat in still water)

⇒ Downstream Speed (d) = 10 + 3 = 13 km/hr

⇒ Time = Distance ÷ Downstream Speed

⇒ Time = 91 ÷ 13

⇒ Time = 7 hr

∴ The correct answer is 7 hr.

Additional Information

Still Water Speed

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

Stream Speed

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

Average Speed

Average speed for a round trip = (Downstream × Upstream) ÷ Still Water Speed.

Calculation:

The total number of students is 500.

Students involved in dancing is 20% of the total students.

⇒ 20% of 500 = 100 students 

Let the students involved in photography be P, those in dancing be D and students involved in singing be S.

⇒ P + S + D = 500      ----(1)

⇒ P + S = 500 - D 

⇒ P + S = 400      ----(2)

It is given that students involved in photography is 60% of students involved in singing

⇒ P =  60 % of S      ----(3)

put the value of P = 60 S/100 in equation (2)

⇒ 60 S /100 + S = 400

⇒ 16 S/10 = 400

⇒ S = 250

⇒ From equation (2) ,

⇒ P + S  = 400

⇒ P + 250  = 400

⇒ P = 150

∴ Number of students involved in photography is 15

Calculation:

From the above question we find out the number of students involved in different activities as follows:

Number of students in dancing = 20% of 500 = 100

Now, Number of students in Singing and Photography = (500 – 100)

⇒ 400

Let number of students in singing be x

Number of students in Photography = 0.6x

So, x + 0.6x = 400

⇒ 1.6x = 400

⇒ x = 250

Singing = 250

Photography = 0.6 × 250 = 150

It is given that the ratio of number of boys to the girls in dancing is 3 : 7

Number of girls in dancing = (7/10) × 100 = 70

Also the number of girls in photography is 87.5 % of the number of boys 

⇒ Boys_(photo) + Girls_(photo) = 150

⇒ Boys_(photo) + 87.5% of boys_(photo) = 150

⇒ 1875 boys_(photo) / 1000 = 150

On solving, we get the value of boys involved in photography = 80

Required difference = (80 – 70)

⇒ 10

∴ The difference between the boys involved in photography and the girls involved in dancing is 10

Calculation:

The number of students involved in different activities is as follows:

Dancing = 100

Singing = 250

Photography = 150

Number of boys in dancing = 3/10 * 100 = 30

Number of girls involved in dancing = 100 - 30 = 70

It is given that the number of girls in singing is 50 less than the boys-

let the number of boys in singing be B and the number of girls be G 

 ⇒B + G = 250      ----(1)

also G = B - 50      ----(2)

On solving the above two equations we get the number of boys in singing as 150 and the number of girls in singing as 100.

Number of girls in photography = 87.5% of boys 

⇒ Number of girls in photography is 70 and the number of boys in photography is 80

Now the total number of girls =  70 + 100 + 70 = 240

and the total number of boys = 30 + 150 + 80 = 260

Hence the ratio will be 240 : 260 = 12 : 13

Calculation:

The number of students involved in different activities are as follows:

Dancing = 100

Singing = 250

Photography = 150

Number of boys in dancing = 3/10 * 100 = 30

Number of girls involved in dancing = 100 - 30 = 70

It is given that the number of girls in singing is 50 less than the boys-

let the number of boys in singing be B and the number of girls be G 

⇒ B + G = 250      ----(1)

also G = B - 50      ----(2)

On solving the above two equations we get the number of boys in singing as 150 and the number of girls in singing as 100.

Number of girls in photography = 87.5% of boys 

⇒ The number of girls in photography is 70 and the number of boys in photography is 80

Number of girls involved in singing =100

Number of boys involved in photography = 80

Required % = 100/80 * 100% = 125%

Calculation:

The number of students involved in different activities is as follows:

Dancing = 100

Singing = 250

Photography = 150

Number of boys in dancing = 3/10 * 100 = 30

Number of girls involved in dancing = 100 - 30 = 70

It is given that the number of girls in singing is 50 less than the boys-

let the number of boys in singing be B and the number of girls be G 

 ⇒B + G = 250      ----(1)

also G = B - 50      ----(2)

On solving the above two equations we get the number of boys in singing as 150 and the number of girls in singing as 100.

Number of girls in photography = 87.5% of boys 

The number of girls in photography is 70 and the number of boys in photography is 80

Number of girls in dancing = 70

Number of girls in singing = 100

Number of girls in photography  = 70

Total number of girls in the class = 70 + 100 + 70 = 240

Shortcut Trick

Area of circle = (22/7) × 7² = 154 cm².

Area of rectangle = 154 − 84 = 70 cm².

Let width = x, then length = x + 3. So, x(x + 3) = 70.

By inspection, 7 × 10 = 70, where 10 − 7 = 3. Thus, length = 10 cm.

∴ The correct answer is 10 cm.

Alternate Method

Given: Radius (r) = 7 cm, Difference in areas = 84 cm², Length (L) = Width (W) + 3 cm.

Formula Used: Area of circle = πr²; Area of rectangle = L × W.

⇒ Area of Circle = (22/7) × 7 × 7 = 154 cm².

⇒ Area of Rectangle = 154 − 84 = 70 cm².

⇒ L × W = 70

⇒ (W + 3) × W = 70

⇒ W² + 3W − 70 = 0

⇒ W² + 10W − 7W − 70 = 0

⇒ W(W + 10) − 7(W + 10) = 0

⇒ W = 7 cm (ignoring negative value)

⇒ Length = 7 + 3 = 10 cm.

∴ The correct answer is 10 cm.

Additional Information

Properties of Rectangles

Perimeter of a rectangle is 2 × (length + width). The diagonals are equal and bisect each other.

Circle Mensuration

Circumference of a circle = 2πr. For a radius of 7 cm, the circumference is always 44 cm and the area is 154 cm².

Quadratic Roots Shortcut

For x² + bx + c = 0, if c is negative, the roots have opposite signs. Find factors of c that differ by b.

Shortcut Trick

For 2 years at 20% interest rate, effective Compound Interest rate = x + y + (xy/100)

Effective rate = 20 + 20 + (20 × 20)/100 = 44%

Total amount received = 100% + 44% = 144% of Principal

Sum received = 14,000 × 1.44 = 20,160

∴ The correct answer is Rs. 20,160.

Alternate Method

Given:

Principal (P) = Rs. 14,000

Rate (R) = 20% per annum

Time (n) = 2 years

Formula Used:

Amount (A) = P[1 + (R/100)]ⁿ

Calculations:

⇒ A = 14,000 × [1 + (20/100)]²

⇒ A = 14,000 × (120/100) × (120/100)

⇒ A = 14,000 × (6/5) × (6/5)

⇒ A = 14,000 × (36/25)

⇒ A = 560 × 36

⇒ A = 20,160

∴ The correct answer is Rs. 20,160.

Additional Information

Compound Interest vs Simple Interest

For the first year, Simple Interest and Compound Interest are the same if interest is compounded annually.

Half-Yearly Compounding

When compounded half-yearly, the rate is halved (R/2) and the time is doubled (2n) in the formula.

Successive Percentage Change

Compound Interest is essentially an application of successive percentage increases on the principal amount.

Shortcut Trick

Total profit = 8700, B's profit = 2700 ⇒ A's profit = 8700 − 2700 = 6000.

Profit Ratio A : B = 6000 : 2700 = 20 : 9.

Time Ratio A : B = 12 months : 6 months = 2 : 1.

Investment Ratio = (Profit ÷ Time) ⇒ A : B = (20 ÷ 2) : (9 ÷ 1) = 10 : 9.

10 units = 5000 ⇒ 1 unit = 500. B's investment = 9 × 500 = 4500.

∴ The correct answer is Rs. 4500.

Alternate Method

Given: A's investment (C_A) = Rs. 5000, A's time (T_A) = 12 months, B's time (T_B) = 6 months, Total Profit = Rs. 8700, B's Profit (P_B) = Rs. 2700.

Formula: Ratio of Profit = (Investment_A × Time_A) : (Investment_B × Time_B)

⇒ Let B's investment be X.

⇒ A's profit = 8700 − 2700 = 6000.

⇒ (5000 × 12) ÷ (X × 6) = 6000 ÷ 2700

⇒ (5000 × 2) ÷ X = 60 ÷ 27

⇒ 10000 ÷ X = 20 ÷ 9

⇒ 20X = 90000 ⇒ X = 4500.

∴ The correct answer is Rs. 4500.

Additional Information

Partnership Basic Principle

Profit is always distributed in the ratio of the product of Investment and Time Period.

Variable Time Investment

If investment amounts are C₁, C₂ for times T₁, T₂, then Profit Ratio P₁:P₂ = C₁T₁ : C₂T₂.

Shortcut Trick

Cost Price (CP) = Rs. 5,100.

Marked Price (MP) = CP × 120/100 = 5,100 × 1.2 = Rs. 6,120.

Selling Price (SP) = Rs. 4,896.

Discount Value = MP − SP = 6,120 − 4,896 = Rs. 1,224.

Discount% = (Discount ÷ MP) × 100 = (1,224 ÷ 6,120) × 100 = 20%.

∴ The correct answer is 20%.

Alternate Method

Given: CP = Rs. 5,100, Markup% = 20%, SP = Rs. 4,896.

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

⇒ Marked Price (MP) = 5100 + 20% of 5100 = 5100 + 1020 = Rs. 6,120.

⇒ Discount Amount = MP − SP = 6120 − 4896 = Rs. 1,224.

⇒ Discount Percentage = (1224 ÷ 6120) × 100.

⇒ Discount Percentage = 1/5 × 100 = 20%.

∴ The correct answer is 20%.

Additional Information

Marked Price & Discount

The Marked Price is the price indicated on the label. Discount is always calculated on the Marked Price, not on the Cost Price.

Markup Percentage

Markup% = [(MP − CP) ÷ CP] × 100. It represents how much more the seller asks for compared to the original cost.

Shortcut Trick

Valid votes = 5000 × 92% = 4600

Winner gets 60% ⇒ Loser gets (100% − 60%) = 40% of valid votes.

Loser votes = 4600 × 40% = 1840 votes.

∴ The correct answer is 1840 votes.

Alternate Method

Given: Total voters = 5000, Rejected votes = 8%, Winner share = 60% of valid votes.

Formula: Valid Votes = Total × (100 − Rejected)%; Loser share = Valid × (100 − Winner%)%

⇒ Total Votes = 5000

⇒ Rejected Votes = 8% of 5000 = (8/100) × 5000 = 400

⇒ Valid Votes = 5000 − 400 = 4600

⇒ Winner Votes = 60% of 4600 = (60/100) × 4600 = 2760

⇒ Loser Votes = 4600 − 2760 = 1840

∴ The correct answer is 1840 votes.

Additional Information

Percentage Calculation

To find x% of y, use (x ÷ 100) × y. For quick calculation, 10% is y/10 and 1% is y/100.

Election Logic

In a two-candidate election, if Winner % is W and Loser % is L, then W + L = 100% of Valid Votes. Majority = (W − L)% of Valid Votes.

Valid vs Invalid Votes

Valid Votes = Total Votes Cast − Invalid/Rejected Votes. Results are always calculated on the basis of Valid Votes unless specified otherwise.

Given: Eight people P, Q, R, S, T, U, V and W are sitting around a circle. All of them are facing the center but not necessarily in the same order.

1. P is sitting to the second of T.

There will be two cases:

2. W is sitting third to the left of P. 3. U is sitting opposite W.

4. R is sitting opposite Q.  5. R is neighbour of neither W nor T.

6. V is not a neighbour of Q. 7. S is sitting next to the left of R. 

Here, case I will be cancelled out as no suitable place for V is left in case I.

So, the final arrangement will be:

Hence, T is sitting third to the right with respect to R.

Given: Eight people P, Q, R, S, T, U, V and W are sitting around a circle. All of them are facing the center but not necessarily in the same order.

1. P is sitting to the second of T.

There will be two cases:

2. W is sitting third to the left of P. 3. U is sitting opposite W.

4. R is sitting opposite Q.  5. R is neighbour of neither W nor T.

6. V is not a neighbour of Q. 7. S is sitting next to the left of R. 

Here, case I will be cancelled out as no suitable place for V is left in case I.

So, the final arrangement will be:

Hence, one person is sitting between Q and W is true.

Given: Eight people P, Q, R, S, T, U, V and W are sitting around a circle. All of them are facing the center but not necessarily in the same order.

1. P is sitting to the second of T.

There will be two cases:

2. W is sitting third to the left of P. 3. U is sitting opposite W.

4. R is sitting opposite Q.  5. R is neighbour of neither W nor T.

6. V is not a neighbour of Q. 7. S is sitting next to the left of R. 

Here, case I will be cancelled out as no suitable place for V is left in case I.

So, the final arrangement will be:

Hence, S is sitting opposite to T.

Given: Eight people P, Q, R, S, T, U, V and W are sitting around a circle. All of them are facing the center but not necessarily in the same order.

1. P is sitting to the second of T.

There will be two cases:

2. W is sitting third to the left of P. 3. U is sitting opposite W.

4. R is sitting opposite Q.  5. R is neighbour of neither W nor T.

6. V is not a neighbour of Q. 7. S is sitting next to the left of R. 

Here, case I will be cancelled out as no suitable place for V is left in case I.

So, the final arrangement will be:

Hence,  R sitting next to the right of S.

Given: Eight people P, Q, R, S, T, U, V and W are sitting around a circle. All of them are facing the center but not necessarily in the same order.

1. P is sitting to the second of T.

There will be two cases:

2. W is sitting third to the left of P. 3. U is sitting opposite W.

4. R is sitting opposite Q.  5. R is neighbour of neither W nor T.

6. V is not a neighbour of Q. 7. S is sitting next to the left of R. 

Here, case I will be cancelled out as no suitable place for V is left in case I.

So, the final arrangement will be:

Hence, 5 persons are sitting between Q and U.

The least possible Venn diagram for the given statements is:

Conclusions:

I. Some stars are sun. → False (No relationship is given between starts and sun, hence this condition is possible but not definite.)

II. Some planet are sun. → True (As it is given that 'only a few sun are planet.' some planets must be sun.)

Hence, only II follows.

The least possible Venn diagram for the given statements is:

Conclusions:

I. Some pens are scales. → False (No relationship is given between pens and scales, hence, it is possible but not definite.)

II. Some scales are pencil. → True (As all scales are pencil is true, some scales are pencil will also be true.)

Hence, only II follows.

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 for the given statements is:

Conclusions:

I. All rectangle being circle is a possibility. → True ( As nothing specific about rectangle and circle is given and none of the given statements is contradicting this possibility, hence the given possibility is true. The possibility diagram is shown below:

II. Some square are triangle. → True ( As some square are circle and all the circle are triangle, hence it is definitely true.)

Both follow.

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.

Given series: MNO  ABD   ATE  POT  KLO

After interchanging the second and the third letters: MON   ADB   AET   PTO    KOL

Hence, 4 words are there which will not end with a vowel.

Given series: MNO  ABD   ATE  POT  KLO

After arranging in alphabetical order: ABD   ATE   KLO   MNO   POT

Hence, KLO will be the third word from the right end.

Given series: MNO  ABD   ATE  POT  KLO

After adding S in each word,

MNOS  ABDS   ATES  POTS  KLOS

Hence, 1 meaningful word will be formed.

Given series: MNO  ABD  ATE  POT  KLO

Words according to the dictionary order: ONM  DBA  TEA  TPO  OLK

Second letter of the third word: E

Second letter of the fourth word: P

Number of letters between E and P according to English Alphabetical series : 10 

Hence, there are 10 letters in the alphabet series between E and P.

Given series:

MNO  ABD   ATE  POT  KLO

After applying the given condition, each consonant is changed to the previous letter in the alphabetic series and vowel remains the same

LMO  AAC  ASE  OOS JKO

The number of words having more than 1 vowel is 3.

Hence, 3 is the correct answer.

The codes are as follows:

Therefore the code for 'weather' is 'rz'.

Hence, rz is the correct answer.

The codes are as follows:

Therefore the code for 'very' is either 'vn' or 'uk'.

Hence, either 1 or 2 is the correct answer.

The codes are as follows:

If the code of 'very high' is 'uk zi'

Therefore the code for 'heavily' is 'vn'

Hence, vn is the correct answer.

The codes are as follows:

Therefore the code for 'it was balmy' is 'ap ku et'.

Hence,'ap ku et' is the correct answer.

Eight friends: A, B, C, D, E, F, G and H

Four month: January, March, April and July

Date : 6th, 17th

1) A delivers his lecture on the 6th of a month which has only 31 days but not in the month of March. 

2. Only three lectures were delivered between A and B.

3) E delivers the lecture immediately after B.

 

 

 

 

 

 

 

 

 

 

 

4. The number of persons who give the lecture after E is the same as the number of persons who give the lecture before F. 

5) Only two persons give lectures between F and C and C is not the last one.

(This will eliminate case 1).

 

 

 

 

 

 

 

 

 

 

 

6) G and C give their lectures in the same month.

7. D gives the lecture before H.

 

 

 

 

 

 

 

 

 

 

 

Hence, D delivers the lecture on 17^th April.

Eight friends: A, B, C, D, E, F, G and H

Four month: January, March, April and July

Date : 6th, 17th

1) A delivers his lecture on the 6th of a month which has only 31 days but not in the month of March. 

2. Only three lectures were delivered between A and B.

3) E delivers the lecture immediately after B.

 

 

 

 

 

 

 

 

 

 

 

4. The number of persons who give the lecture after E is the same as the number of persons who give the lecture before F. 

5) Only two persons give lectures between F and C and C is not the last one.

(This will eliminate case 1).

 

 

 

 

 

 

 

 

 

 

 

6) G and C give their lectures in the same month.

7. D gives the lecture before H.

 

 

 

 

 

 

 

 

 

 

 

Hence, A deliver the lecture immediately after D.