SBI PO Prelims Memory Based Paper (Held on:25 June 2018) (Previous Year Paper)

The correct answer is 'Only (i)'.

Key Points

• The given two sentences are only connected with the connector 'As' to make a meaningful sentence.
• 'As' is an adverb that is used to give the reason.
• From the second sentence, We can conclude that the president declared the emergency but the reason is the first sentence hence we need to use an adverb to tell the reason.
• From the third sentence, it can not be possible because 'being' is used, it means the subject 'the country' has already known so we can't use 'being as a state'

Out of the given three options, the two sentences can be joined into a single sentence as:- 'As the country was in a state of deep turmoil, the President declared an emergency.'​

The correct answer is 'Only (iii)'.

Key Points

Out of the given three options, the two sentences can be joined correctly in two ways: 'As soon as the police arrived at the railway station, the suspect saw them, fired three bullets, and ran away'.

The correct answer is 'Only (i)'.

Key Points

Out of the given three options, the given sentences can be joined correctly as: 'When Indira Gandhi was assassinated in 1984, Rajiv Gandhi became the Prime Minister'.

Thus, only option (i) is correct.

The correct answer is option 1, i.e., 'Only (i)'.

• Out of the given three options, the two sentences can be joined in only one way: 'Unless the Central Government cuts down on the defence budget, the financial crisis will not be resolved'.

• Thus, only option (i) is correct. 

• We use the conjunction unless to mean ‘except if’. The clause which follows unless is a subordinate clause (sc): it needs the main clause (mc) to make a complete sentence.

• Unless is a conditional word (like if), so we don’t use will or would in the subordinate clause:

• Unless I hear from you, I’ll see you at two o’clock.

• Not: Unless I’ll hear from you …

• We use unless to introduce an extra thought or piece of information:

• He didn’t even know about the crash – unless he’d heard about it on the radio.

The correct answer is option 3, i.e., 'Both (ii) and (iii)'.

Out of the given three options, the two sentences can be joined in two ways: 'While he has failed many times and almost all his plans have seen little success, he still hopes to succeed one day' and 'In spite of the fact that he has failed many times and almost all his plans have seen little success, he still hopes to succeed one day'.

However, option 1 does make a meaningful sentence but changes the meaning of the context. 

Thus, only options (ii) and (iii) are correct.

The correct answer is A-E 

Key Points

In the given question we have to find out the following:

• Which sentence from Column 1 joined with a sentence from Column 2 gives a contextually and grammatically correct sentence.
• Looking at the option we find that A-E is the only one that forms a proper coherent sentence. 
• Blowing the horn loudly in form of school is strictly forbidden by law.
• ​The other options given fail to create a contextually and grammatically correct sentence.
• Thus the correct answer is A-E​

​

Reading the second option B-D:

• We might think that the sentence The pollution has made every trees dirty sound correct.
• But this sentence is wrong as it is not grammatically correct. 
• The noun that comes after the word 'every' should always be singular.
• Here the word trees is plural making it grammatically incorrect.

The correct answer is 2.

Sentence A, when joined with D, gives the meaning that the government must protect the rights of the people.

Sentence B, when joined with F, gives the meaning that the children are having summer holidays.

The correct answer is 3.

Sentence A, when joined with E, gives the meaning that the young generation has much more knowledge of computers.

The correct answer is 2.

Sentence B, when joined with D, gives the meaning that germs grow where water has been stored for a period of time.

The correct answer is 3.

Sentence C, when joined with D, gives the meaning that looking after the needs of the poor people is something that brings out the kindness in a person.

'Than' suggests comparative degree and so, we cannot use 'nice'. We do not use 'very nice than' for comparison. 'More nicer' is not used as the use of two intensifies, more and +er is incorrect in standard English. The correct answer is much nicer.

The correct answer is No improvement.

Key Points

The man next door- this phrase refers to the man who is the next-door neighbour of the subject in this sentence.

So, the answer is 5.

The other options, all of which have apostrophes do not make any sense whatsoever.

Advice is an uncountable noun and so, we cannot use 'an advice' or 'a few advice'. 'The' is used to specify and so 'the advice' is not appropriate in the context of the sentence. The correct answer is a piece of advice.

With 'accused', we use the preposition 'of' and we do not use any other prepositions.

One can accuse someone of doing something. Accused for is used when referring to a 3rd party or on behalf of.

Hence, the correct answer is accused the government of.

'To give up' means to stop making an effort and accept defeat, 'give way' means 'to collapse or to be replaced by (something)', 'give off' means 'to produce' and 'give forth' means 'to announce or to send out'. The appropriate answer is give up on.

When used to emphasise something, 'only' is placed next to the word which one intends to emphasise. In the given sentence, the emphasis is on the noun, 'bike' and not the verb, 'bought'.

So, the correct answer is 'bought not only'.

The correct answer is see any gain.

Key Points

This question deals with the concept of double negatives. 

Using 'no gain' after 'cannot see' is grammatically incorrect in standard British English and we have to replace 'no gain' with 'any gain' to make the sentence correct.

Additional Information 

In standard English, each subject-predicate construction should only have one negative form. 

• I will not bake a cake.(correct)
• I cannot go nowhere tonight(incorrect)
• We are not planning a trip(correct)

The correct answer is discussed.

Key Points

• In the sentence, 'discuss' is a transitive verb and transitive verbs do not require a preposition.

Correct sentence: "We discussed the matter yesterday." 

Additional Information

• A transitive verb requires a direct object to complete its meaning—an 'agent' performs an action and a "patient" ( or "theme") undergoes the action.

• The direct object usually takes the form of a noun phrase.

• A transitive verb is a verb that requires an object to receive the action.

• Example:

• Correct: The speaker discussed different marketing strategies in the video. 

• Incorrect:  The speaker discussed in the video.

• The verb "discuss" requires an object ("different marketing strategies"). It is necessary to state what the speaker discussed.

The correct option is Option 3, i.e., ‘poor flood planning and its casualties’.The given option is correct because the title encompasses almost all the ideas in the passage and conveys the central idea. The other options are an aspect of the passage and do not give a full idea. Hence, the correct option is Option 3.

The correct option is Option 4, i.e., ‘unresponsive’.The word ‘sclerotic’ is used in the passage to define the state of urban planning as ‘rigid and non-adaptive’. The word most similar in meaning, is, therefore, ‘unresponsive’ as the other options have an entirely different meaning. Hence, the correct option is Option 4.

The correct option is Option 1.After reading the passage, it is clear that Options 2 & 3 are incorrect and the exact opposite has been stated in the passage. For Option 2, the word ‘retrograde’ in the passage signifies that sanctioning of large estate projects without an environmental impact is harmful. Option 4 is simply wrong. Therefore, the correct option is Option 1.

The correct option is Option 3, i.e., ‘Assessment and preparation of damage estimates are done, along with expensive restoration work’.From the first paragraph of the passage, it is seen that after the waters recede, the cycle of assessment of the damage, preparation of loss estimates and expensive restoration work begins. Therefore, the correct option is Option 3.

The correct option is Option 2, i.e., ‘flooded’.‘Swollen’ in the context means ‘a river overflowing with water’. The word ‘flooded’ is synonymous to ‘swollen’ in the context of the passage, making it an obvious choice. The other words are not similar in meaning. Therefore, the correct option is Option 2.

The correct answer is Option 2, i.e., ‘Research on flood preparation and urban planning have gone to waste and no solution is at hand’.Option 1 lays down the premise of the passage but does not form the key idea. Similarly, Option 3 is a statement mentioned in the passage and does not form the underlying idea. Option 4 is the conclusion of the passage but not the summary.Option 2 is the best choice because after reading the passage, one understands that the flood preparation and urban planning done to avoid such a situation have gone to waste and people are suffering. Therefore, the correct option is Option 2.

The correct answer is ADBC.

Key Points

• The sentence is about the ease of communication in the digital era. Therefore, A is the second part.
• Part D discusses the effect of it. Therefore, the next part is D.
• B comes after D as it informs us that the ability to talk to each other has not been increased.
• C is the last part because the actual effect of the ease of communication is mentioned.
• Hence, option 4) is the answer.

The given parts of the sentence when arranged in the correct sequence: ADBC stands ‘The ease of communication in the digital era has not increased our ability to talk to each other, instead we talk at each other.’

The correct answer is 2.

The given parts of the sentence when arranged in the correct sequence: ADBC stands ‘The Supreme Court attempted to narrow the scope of provisions holding that membership was limited to cases where an individual was engaged in active incitement to violence’.

The correct answer is option 5.

The given parts of the sentence are already in the correct sequence.

The correct answer is 3.

The given parts of the sentence when arranged in the correct sequence: BCDA stands as’ The report said that the state government had told that landowners whose properties had to be acquired for the proposed highway would be paid fantastic compensation.

The correct answer is ACDB.

Key Points

The given parts of the sentence when arranged in the correct sequence: ACDB stands as

'If computers and advanced technologies help the agricultural universities to advise farmers on the best practices that can be used to increase crop yield and quality of the crops, then India could see a farming revolution in the future’.

The correct answer is CDBA​.

Key Points

The given parts of the sentence when arranged in the correct sequence: CDBA stands as’ In agriculture, for example, machine will provide information to the farmers on the quality of the soil when to sow, where to spray herbicide, and when to expect pest infestations’.

The pattern of given series is:

⇒ 6 – 5.9 = 0.1 = 0.1

⇒ 6.1 – 6 = 0.1 = 0.1 × 1

⇒ 6.4 – 6.1 = 0.3 = 0.1 × 3

⇒ 7.9 – 6.4 = 1.5 = 0.3 × 5

⇒ 18.4 – 7.9 = 10.5 = 1.5 × 7 (not 18.5)

⇒ 112.9 – 18.4 = 10.5 × 9 = 94.5

∴ Wrong number in series = 18.5

The pattern of given series is:

⇒ 26 – 26 = 1² – 1 = 0 (not 27)

⇒ 34 – 26 = 3² – 1 = 8

⇒ 58 – 34 = 5² – 1 = 24

⇒ 106 – 58 = 7² – 1 = 48

⇒ 186 – 106 = 9² – 1​ = 80  

⇒ 306 – 186 = 11² – 1​ = 120

∴ Wrong number in series is 27.

1 × 1 + 2 = 3

⇒ 3 × 2 + 3 = 9

⇒ 9 × 3 + 4 = 31

⇒ 31 × 4 + 5 = 129

⇒ 129 × 5 + 6 = 651 (not 652)

⇒ 651 × 6 + 7 = 3913

∴ Wrong number in series = 652

330 – 80 = 250

⇒ 280 – 80 = 200

⇒ 280 – 120 = 160

⇒ 250 – 120 = 130

⇒ 250 – 140 = 110 (not 130)

⇒ 240 – 140 = 100

(250 – 200 = 50, 200 – 160 = 40, 160 – 130 = 30, 130 – 110 = 20, 110 – 100 = 10)

∴ Wrong number in series = 130

Alternate Method

There is one more solution which is faster 330, 80, 280, 120, 250, 130, 240

Difference of alternate numbers

330-280=50

120-80=40

280-250=30

130-120=10(should be 20)

250-240=10

291 – 147 = 144

⇒ 147 – 75 = 72

⇒ 75 – 39 = 36

⇒ 39 – 21 = 18 (not 22)

⇒ 21 – 12 = 9

⇒ 12 – 7.5 = 4.5

∴ Wrong number in series = 22

2^? = 32.01 ÷ 128.01 × 1023.97 ÷ 7.97

By approximation;

⇒ 2^? = 32 ÷ 128 × 1024 ÷ 8 = 32 ÷ 128 × 128

2^? = 32 = 2⁵

⇒ ? = 5

339.98 ÷ ? = √143.98 + √64.02

By approximation;

⇒ 340 ÷ ? = √144 + √64 = 20

⇒ ? = 340/20 = 17

34.03% of 550.08 ÷ ? = 297.08 + √728.97 - √89998

By approximation;

⇒ 34% of 550 ÷ ? = 297 + √729 - √90000

187 ÷ ? = 297 + 27 - 300 = 24

⇒ ? = 8 (approx.)

(? ÷ 9.97) × 12.08 = 20.12% of 1319.98

By approximation;

(? ÷ 10) × 12 = 20% of 1320

? ÷ 10 × 12 = 264

⇒ ? = 264 × 10/12 = 220

?% of 179.98 = √((24.03)² + (17.99)² + (60.02% of 659.96))

By approximation;

?% of 180 = √((24)² + (18)² + (60% of 660))

?% of 180 = √(576 + 324 + 396) = √1296 = 36

⇒ ?% = 36/180 = 1/5

⇒ ? = 20

Total number of pens sold on Tuesday = 95

Total number of pens sold on Wednesday = 50

∴ Required % = (95 - 50)/50 × 100 = 90%

The total number of non-defective pens sold on Wednesday = (100 - 6)/100 x 50 = 47

The total number of non-defective pens sold on Thursday = (100 - 5)/100 × 60 = 57

∴ Total number of non-defective pens sold on Wednesday and Thursday together = 47 + 57 = 104

The total number of pens sold on Monday = 45

The total number of pens sold on Saturday = 80

The total number of pens sold on Sunday = (100 – 12.5)/100 × 80 = 70

∴ The total number of pens sold on Sunday and Monday together = 45 + 70 = 115

The total number of pens sold on Thursday, Friday and Saturday together = 60 + 75 + 80 = 215

The total number of pens sold on Monday, Tuesday and Wednesday together = 45 + 95 + 50 = 190

∴ Required difference = 215 - 190 = 25

Let total number of pens sold on Sunday = x

So, according to the question,

Total number of pens sold on Sunday = (100 + 25)/100 × x

⇒ 80 = 125/100 × x

⇒ x = 8000/125 = 64

So, total number of pens sold on a week = 45 + 95 + 50 + 60 + 75 + 80 + 64 = 469

∴ Required average = 469/7 = 67

Quantity A:

Probability of getting green ball is 1/4

We know that, Probability = Favourable outcomes/Total outcomes

Probability = x/(12 + x)

1/4 = x/(12 + x)

3x = 12

x = 4

Quantity B = 4

Hence Quantity A = Quantity B

First we will find Quantity A,

Quantity A:

Here, Cost price (CP) = 140 and

Selling Price (SP) = 168

% Profit = (SP – CP)/CP × 100

⇒ % Profit = (168 – 140)/140 × 100 = 20

Now,

Quantity B:

Here, Marked Price (MP) = 2000

Selling Price (SP) = 1800

% Discount = (MP – SP)/MP × 100

⇒ % Discount = (2000 – 1800)/2000 × 100 = 10

Clearly, Quantity B < Quantity A

Firstly we will find Quantity A,

Quantity A:

Number of ways to choose 2 students from 5 students = ⁵C₂ = 10

Number of ways to choose 2 teachers from 3 teachers = ³C₂ = 3

Number of ways to choose 1 coach from 2 coaches = ²C₁ = 2

∴ Total number of ways = 10 × 3 × 2 = 60

Now,

Quantity B:

Total number of people = 5 + 3 + 2 = 10

Number of ways to choose 5 people from 10 people = ¹⁰C₅ = 252

Quantity B > Quantity A

We know that LCM is always a multiple of HCF.

Let LCM = k(HCF)

⇒ HCF + k(HCF) = 37

⇒ (k + 1)(HCF) = 37

Possible values of k are 0 and 36.

If k = 0, HCF = 37, which is not possible as LCM will become 0.

If k = 36, HCF = 1, and LCM = 36.

So, P and Q can be 1 and 36, or 4 and 9.

If they are 1 and 36, their sum is 37 and product is 36.

If they are 4 and 9, their sum is 13 and product is 36.

So, sum can be lesser or greater than product.

No relation between A and B can be established.

Shortcut Trick Quantity A: Works done = Total Time ÷ Time per homework = 6 ÷ 2 = 3. Quantity B: LCM of 20, 25, 10 = 100. Efficiencies: A = 5, B = 4, C = 10. Work in 9 days = (5 + 4) × 9 = 81. Remaining work = 100 − 81 = 19. Remaining days = 19 ÷ (5 + 4 + 10) = 19 ÷ 19 = 1. Since 3 > 1, Quantity A > Quantity B. ∴ The correct answer is Quantity A > Quantity B. Alternate Method Quantity A: Given: Time for 1 homework = 2 hours, Total time = 6 hours. ⇒ Number of home-works = 6 ÷ 2 ⇒ Quantity A = 3 home-works Quantity B:

Person Days Total Work Efficiency

A 20 100 5

B 25 4

C 10 10

⇒ Combined efficiency of A and B = 5 + 4 = 9 units/day ⇒ Work done by A and B in 9 days = 9 × 9 = 81 units ⇒ Remaining work = 100 − 81 = 19 units ⇒ Combined efficiency of A, B, and C = 5 + 4 + 10 = 19 units/day ⇒ Remaining days = 19 ÷ 19 = 1 day ⇒ Quantity B = 1 day Comparing A and B: 3 > 1 ∴ The correct answer is Quantity A > Quantity B. Additional Information Total Work Formula Total Work = Efficiency × Time. Using the LCM of individual times as Total Work simplifies efficiency calculations. Comparison of Quantities In Quantity Comparison questions, ensure both quantities are evaluated in their respective units before establishing the relation (>, <, or =).

Shortcut Trick

Given: Total volume = 5040π cm³ and Height (h) = 20 cm.

Volume of cylinder = π × 12² × 20 = 2880π cm³.

Volume of cone = 5040π − 2880π = 2160π cm³.

Since Volume of cone = (1/3) × π × r_A² × 20 = 2160π ⇒ r_A² = 324 ⇒ r_A = 18 cm.

Ratio of radii = 18 : 12 = 3 : 2.

∴ The correct answer is 3 : 2.

Alternate Method

Given:

Height of cone and cylinder (h) = 20 cm

Radius of cylinder (r_H) = 12 cm

Total Volume = 5040π cm³

Formula Used:

Volume of Cone = (1/3)πr²h

Volume of Cylinder = πr²h

Calculations:

⇒ Volume of Cylinder (H) = π × (12)² × 20 = 2880π cm³

⇒ Volume of Cone (A) = Total Volume − Volume of Cylinder

⇒ Volume of Cone (A) = 5040π − 2880π = 2160π cm³

⇒ (1/3) × π × r_A² × 20 = 2160π

⇒ r_A² = (2160 × 3) ÷ 20

⇒ r_A² = 108 × 3 = 324

⇒ r_A = √324 = 18 cm

⇒ Ratio = r_A : r_H = 18 : 12

⇒ Ratio = 3 : 2

∴ The correct answer is 3 : 2.

Additional Information

Volume of Mensuration Shapes

For a given height and radius, the volume of a cylinder is exactly 3 times the volume of a cone.

Curved Surface Area

CSA of Cylinder = 2πrh | CSA of Cone = πrl, where l = √(r² + h²) is the slant height.

Ratio Property

If heights are equal, the ratio of volumes of two cylinders or cones is equal to the ratio of the squares of their radii.

Shortcut Trick

Total current age of X and Y = 86 + (7 × 2) = 100 years.

Difference between X and Y age = 20 − 4 = 16 years (X is older).

Present age of Y = (Sum − Difference) ÷ 2 = (100 − 16) ÷ 2 = 42 years.

Age of Y four years hence = 42 + 4 = 46 years.

∴ The correct answer is 46 years.

Alternate Method

Given:

(X − 7) + (Y − 7) = 86

X − 20 = Y − 4

Calculations:

⇒ X + Y − 14 = 86

⇒ X + Y = 100 --- (Eq. 1)

⇒ X − Y = 20 − 4

⇒ X − Y = 16 --- (Eq. 2)

⇒ Adding Eq. 1 and Eq. 2: 2X = 116 ⇒ X = 58

⇒ Subtracting Eq. 2 from Eq. 1: 2Y = 84 ⇒ Y = 42

⇒ Age of Y 4 years hence = Y + 4 = 42 + 4 = 46 years

∴ The correct answer is 46 years.

Additional Information

Sum of Ages in Past/Future

If the sum of ages of 'n' persons 't' years ago was S, then their present sum is S + (n × t).

Age Difference Constant

The difference between the ages of two people remains constant regardless of the number of years passed or future time.

Finding Individual Values from Sum and Difference

If Sum = S and Difference = D, then Larger value = (S + D) ÷ 2 and Smaller value = (S − D) ÷ 2.

Shortcut Trick

Speed of Train A = (140 + 180) ÷ 16 = 320 ÷ 16 = 20 m/s.

Ratio of speeds (B : A) = 3 : 2 ⇒ Speed of Train B = 20 × (3/2) = 30 m/s.

Length of Train B = Speed of B × Time to cross man = 30 × 15 = 450 m.

∴ The correct answer is 450 m.

Alternate Method

Given:

Length of Train A (L_A) = 140 m, Length of Platform (L_P) = 180 m.

Time taken by A (T_A) = 16 s, Ratio of speeds (S_B : S_A) = 3 : 2.

Time taken by B to cross a man (T_B) = 15 s.

Formula Used:

Speed = Total Distance ÷ Total Time

Length of Train = Speed × Time (when crossing a stationary point object)

Calculations:

⇒ Speed of Train A (S_A) = (L_A + L_P) ÷ T_A

⇒ S_A = (140 + 180) ÷ 16 = 320 ÷ 16 = 20 m/s

⇒ Speed of Train B (S_B) = (3 ÷ 2) × 20 = 30 m/s

⇒ Length of Train B = S_B × T_B

⇒ Length of Train B = 30 × 15 = 450 m

∴ The correct answer is 450 m.

Additional Information

Relative Speed

When two objects move in opposite directions, relative speed = S₁ + S₂. In the same direction, relative speed = |S₁ − S₂|.

Train Crossing Objects

To cross a pole/man, distance = length of train. To cross a bridge/platform, distance = length of train + length of object.

Unit Conversion

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

Shortcut Trick

Difference between Downstream and Upstream speed is 2 × Stream Speed.

2 × Stream Speed = 6 km/hr ⇒ Stream Speed = 3 km/hr.

Upstream Speed = Boat Speed − Stream Speed = 21 − 3 = 18 km/hr.

Required Time = Distance ÷ Upstream Speed = 108 ÷ 18 = 6 hours.

∴ The correct answer is 6 hr.

Alternate Method

Given:

Speed of boat (u) = 21 km/hr

Let speed of stream = v km/hr

Downstream speed (D) = u + v = 21 + v

Upstream speed (U) = u − v = 21 − v

Formula Used:

Time = Distance ÷ Speed

Difference (D − U) = 6 km/hr

Calculations:

⇒ (21 + v) − (21 − v) = 6

⇒ 2v = 6 ⇒ v = 3 km/hr

⇒ Upstream speed (U) = 21 − 3 = 18 km/hr

⇒ Time = 108 ÷ 18

⇒ Time = 6 hr

∴ The correct answer is 6 hr.

Additional Information

Downstream and Upstream Speed

Downstream speed (a) = u + v and Upstream speed (b) = u − v, where u is speed in still water and v is stream speed.

Boat and Stream Speed Formulas

Speed of boat (u) = (a + b) ÷ 2 and Speed of stream (v) = (a − b) ÷ 2.

Average Speed in Still Water

Average speed for a round trip is (Downstream × Upstream) ÷ Boat speed.

Shortcut Trick

Total letters in ABJURED = 7. Total arrangements = 7!

Vowels (A, U, E) = 3; Consonants (B, J, R, D) = 4.

Treat (AUE) as 1 unit. Total units = 4 + 1 = 5. Arrangements = 5! × 3!

Probability = (5! × 3!) ÷ 7! = (120 × 6) ÷ 5040 = 720 ÷ 5040 = 1/7.

∴ The correct answer is 1/7.

Alternate Method

Given: Word = ABJURED. Letters = 7 (A, B, J, U, R, E, D).

Formula Used: Probability = (Favorable outcomes) ÷ (Total outcomes)

⇒ Total outcomes n(S) = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

⇒ Vowels = A, U, E (3 letters). Consonants = B, J, R, D (4 letters).

⇒ Bundle 3 vowels together as one unit. Total items to arrange = 4 consonants + 1 unit = 5 items.

⇒ Arrangements of these 5 items = 5! = 120.

⇒ Internal arrangement of 3 vowels = 3! = 6.

⇒ Favorable outcomes n(E) = 5! × 3! = 120 × 6 = 720

⇒ Probability P(E) = 720 ÷ 5040 = 1/7

∴ The correct answer is 1/7.

Additional Information

Arrangement of n items

The number of ways to arrange n distinct objects is n! (n-factorial).

String Method (Always Together)

To keep specific items together, tie them in a single bundle and arrange that bundle with the remaining items.

Vowels Never Together

Calculated as (Total arrangements − Arrangements where vowels are always together).

Number of workers = (Percentage of workers) × (Total Workers)

Number of officers = (Ratio of officers : workers) × (number of workers)

Number of officers in A and B together = 18 + 22 = 40

Number of officers in B and C together = 22 + 18 = 40

Thus, the ratio of officers of company A and B together to the officers of company B and C together = 1 : 1

Note that, here, the pie chart given is based on total workers and in the table below the ratio given is of officers ∶  workers.

So, we are to equate the part of workers in the ratio to the number of workers obtained from pie chart.

If you take total workers mistakenly as total employees then the entire solution will be wrong.

Percentage difference = ((final - initial)/initial) × 100%

= ((418 - 234)/234) × 100% = 78.63% ≈ 79%

Note that, here, the pie chart given is based on total workers and in the table below the ratio given is of officers ∶  workers.

So, we are to equate the part of workers in the ratio to the number of workers obtained from pie chart.

If you take total workers mistakenly as total employees then the entire solution will be wrong.

Percentage of officers of company A = $\frac{{18}}{{958}} \times$ 100% = 1.88%

Converting it to degrees,

1.88% of 360° = 6.76°

Note that, here, the pie chart given is based on total workers and in the table below the ratio given is of officers ∶  workers.

So, we are to equate the part of workers in the ratio to the number of workers obtained from pie chart.

If you take total workers mistakenly as total employees then the entire solution will be wrong.

Number of workers of company C = 24% of 900

Number of workers of company B = 44% of 900

Ratio of number of workers of company C to that of company B = 24% of 900 : 44% of 900 = 24 : 44 = 6 : 11

ALTERNATIVE METHOD:

In this type of questions, where percentage is known and ratio or percentage is asked. then there is no need to use the real values.

∴ Required Ratio = 24 : 44 = 6 : 11

Officers of company A and C together = 18 + 18 = 36

Workers of company B = 396

Ratio of officers of company A and C together workers of company B = 36 : 396 = 1 : 11

Note that, here, the pie chart given is based on total workers and in the table below the ratio given is of officers ∶  workers.

So, we are to equate the part of workers in the ratio to the number of workers obtained from pie chart.

If you take total workers mistakenly as total employees then the entire solution will be wrong.

In third year,

A’s investment = Rs. 50000 for 12 months

B’s investment = Rs. 40000 for 12 months

C’s investment = Rs. 60000 for 12 months

Hence,

⇒ A’s share : B’s share : C’s share = 50000 : 40000 : 60000

⇒ A’s share : B’s share : C’s share = 5 : 4 : 6

∴ C’s share = (6/15) × 60000 = Rs. 24000

In second year,

A’s investment = Rs. 50000 for 12 months

C’s investment = Rs. 60000 for (12 – 3) = 9 months

C’s share = Rs. 4500

Hence,

⇒ (50000 × 12) : (60000 × 9) = A’s share : 4500

⇒ 10 : 9 = A’s share : 4500

⇒ A’s share = (10/9) × 4500

∴ A’ share = Rs. 5000

A’s investment = Rs. 50000 for 12 months

B’s investment = Rs. 40000 for (12 – 4) = 8 months

∴ Ratio of their share in profit = (50000 × 12) : (40000 × 8) = 15 : 8

Let B invested in the company after ‘x’ months

A’s investment = Rs. 50000 for 12 months

B’s investment = Rs. 40000 for (12 – x) months

A’s share = Rs. 12000

B’s share = Rs. 5600

Hence,

⇒ (50000 × 12) : [40000 × (12 – x) ] = 12000 : 5600

⇒ (5 × 12) : [4 × (12 – x) ] = 120 : 56

⇒ 60 : (48 – 4x) = 120 : 56

⇒ (60 × 56)/120 = 48 – 4x

⇒ 28 = 48 – 4x

⇒ 4x = 20

⇒ x = 5

∴ B invested in the company after 5 months

As the time duration for which B invested his money is not known, his share of profit couldn’t be determined.

Seven boxes: D, E, F, G, H, I and J.

No. of articles: 3, 7, 10, 13, 17, 18 and 20.

1. There are two boxes between G and the box in which there are 13 articles.

2. G lies above the box having 13 articles.

3. G is placed below D.

4. I is immediately below the box which has 17 articles.

5. D doesn’t have 17 articles.

6. There are two boxes between the boxes having 17 and 7 articles.

7. Two boxes are placed between D and the box in which there are 10 articles.

8. There are only three boxes between H and the box which have 10 articles.

(Combining all, we have four possible cases)

Case 1:

Case 2:

Case 3:

Case 4:

9. Only one box is there between E and J.

(There will be seven possible cases)

10. E does not have 7 no. of articles.

Case 1:

Case 2:

Case 3:

Case 4:

Case 5:

Case 6:

Case 7:

11. The difference between no. of articles in boxes G and just above G is 13.

(Hence, Case 1, 2, 3, 4, 6 and 7 will be eliminated, we can further proceed with Case 5)

12. The number of articles in the box which is just above J is less than the no. of articles in J.

Clearly, box E has 18 no. of articles is wrong.

Seven boxes: D, E, F, G, H, I and J.

No. of articles: 3, 7, 10, 13, 17, 18 and 20.

1. There are two boxes between G and the box in which there are 13 articles.

2. G lies above the box having 13 articles.

3. G is placed below D.

4. I is immediately below the box which has 17 articles.

5. D doesn’t have 17 articles.

6. There are two boxes between the boxes having 17 and 7 articles.

7. Two boxes are placed between D and the box in which there are 10 articles.

8. There are only three boxes between H and the box which have 10 articles.

(Combining all, we have four possible cases)

Case 1:

Case 2:

Case 3:

Case 4:

9. Only one box is there between E and J.

(There will be seven possible cases)

10. E does not have 7 no. of articles.

Case 1:

Case 2:

Case 3:

Case 4:

Case 5:

Case 6:

Case 7:

11. The difference between no. of articles in boxes G and just above G is 13.

(Hence, Case 1, 2, 3, 4, 6 and 7 will be eliminated, we can further proceed with Case 5)

12. The number of articles in the box which is just above J is less than the no. of articles in J.

Clearly, Box H is immediately above the box which contains 3 articles.

Seven boxes: D, E, F, G, H, I and J.

No. of articles: 3, 7, 10, 13, 17, 18 and 20.

1. There are two boxes between G and the box in which there are 13 articles.

2. G lies above the box having 13 articles.

3. G is placed below D.

4. I is immediately below the box which has 17 articles.

5. D doesn’t have 17 articles.

6. There are two boxes between the boxes having 17 and 7 articles.

7. Two boxes are placed between D and the box in which there are 10 articles.

8. There are only three boxes between H and the box which have 10 articles.

(Combining all, we have four possible cases)

Case 1:

Case 2:

Case 3:

Case 4:

9. Only one box is there between E and J.

(There will be seven possible cases)

10. E does not have 7 no. of articles.

Case 1:

Case 2:

Case 3:

Case 4:

Case 5:

Case 6:

Case 7:

11. The difference between no. of articles in boxes G and just above G is 13.

(Hence, Case 1, 2, 3, 4, 6 and 7 will be eliminated, we can further proceed with Case 5)

12. The number of articles in the box which is just above J is less than the no. of articles in J.

Clearly, box D contains 3 articles.

Seven boxes: D, E, F, G, H, I and J.

No. of articles: 3, 7, 10, 13, 17, 18 and 20.

1. There are two boxes between G and the box in which there are 13 articles.

2. G lies above the box having 13 articles.

3. G is placed below D.

4. I is immediately below the box which has 17 articles.

5. D doesn’t have 17 articles.

6. There are two boxes between the boxes having 17 and 7 articles.

7. Two boxes are placed between D and the box in which there are 10 articles.

8. There are only three boxes between H and the box which have 10 articles.

(Combining all, we have four possible cases)

Case 1:

Case 2:

Case 3:

Case 4:

9. Only one box is there between E and J.

(There will be seven possible cases)

10. E does not have 7 no. of articles.

Case 1:

Case 2:

Case 3:

Case 4:

Case 5:

Case 6:

Case 7:

11. The difference between no. of articles in boxes G and just above G is 13.

(Hence, Case 1, 2, 3, 4, 6 and 7 will be eliminated, we can further proceed with Case 5)

12. The number of articles in the box which is just above J is less than the no. of articles in J.

Clearly, 20 articles are there in box ‘G’.

Seven boxes: D, E, F, G, H, I and J.

Number of articles: 3, 7, 10, 13, 17, 18 and 20.

1. There are two boxes between G and the box in which there are 13 articles.

2. G lies above the box having 13 articles.

3. G is placed below D.

4. I is immediately below the box which has 17 articles.

5. D doesn’t have 17 articles.

6. There are two boxes between the boxes having 17 and 7 articles.

7. Two boxes are placed between D and the box in which there are 10 articles.

8. There are only three boxes between H and the box which have 10 articles.

(Combining all, we have four possible cases)

Case 1:

Case 2:

Case 3:

Case 4:

9. Only one box is there between E and J.

(There will be seven possible cases)

10. E does not have 7 number of articles.

Case 1:

Case 2:

Case 3:

Case 4:

Case 5:

Case 6:

Case 7:

11. The difference between the number of articles in box G and just above G is 13.

(Hence, Case 1, 2, 3, 4, 6 and 7 will be eliminated, we can further proceed with Case 5)

12. The number of articles in the box which is just above J is less than the number of articles in J.

Clearly, there are two boxes between G and I.