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Chain Rule - Aptitude Questions and Answers - RejinpaulPlacement

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1.
If 15 toys cost Rs. 234, what do 35 toys cost?
Answer & Solution
Answer: b) Rs. 546

Solution:   Let the required cost be Rs. x. Then,

More toys, More Cost. (Direct Proportion)

15 : 35 ::234 : x
=> [15 * x] = [35 * 234]
=> x = [(35 * 234) / 15] = 546.

Hence, the cost of 35 toys is Rs. 546.
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2.
If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?
Answer & Solution
Answer: c) 60 hours

Solution:   Let the required number of hours be x. Then,

Less men, More hours. (Indirect Proportion)

15 : 36 :: 25 : x
=> (15 * x) = (36 * 25)
=> x = [(36 * 25) / 15] = 60.

Hence, 15 men can do it in 60 hours.
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3.
If the wages of 6 men for 15 days be Rs. 2100, then find the wages of 9 men for 12 days.
Answer & Solution
Answer: c) Rs. 2520

Solution:   Let the required wages be Rs. x.

More men, More wages. (Direct Proportion)
Less days, Less wages. (Direct Proportion)

Men 6 : 9
Days 15 : 12 :: 2100 : x

(6 * 15 * x) = (9 * 12 * 2100)
=> x = [(9 * 12 * 2100) / (6 * 15)] = 2520.

Hence, the required wages are Rs. 2520.
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4.
If 20 men can build a wall 56 metres long in 6 days, what length of a similar wall can be built by 35 men in 3 days?
Answer & Solution
Answer: b) 49 m

Solution:   Let the required length be x metres.

More men, More length built. (Direct Proportion)

Less days, Less length built. (Direct Proportion)

Men 20 : 35
Days 6 : 3     :: 56 : x

(20 * 6 * x) = (35 * 3 * 56)
=> x = [(35 * 3 * 56) / 120] = 49.

Hence, the required length is 49 m.
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5.
If 5 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?
Answer & Solution
Answer: d) 15

Solution:   Let the required number of days be x.

More men, Less days. (Indirect Proportion).
Less hours per day, More days. (Indirect Proportion)

Men                 18 : 15
Hours per days 8 : 9     :: 16 : x

(18 * 8 * x = (15 * 9 * 16)
=> x = [(15 * 144) / 144 ] = 15.

Hence, the required number of days = 15.
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6.
If 9 engines consume 24 metric tonnes of coal, when each is working 8 hours a day, how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?
Answer & Solution
Answer: c) 26

Solution:   Let 3 engines of former type consume 1 unit in 1 hour.
Then, 4 engines of latter type consume 1 unit in 1 hour.

1 engine of former type consumes 1/3 unit in 1 hour.
1 engine of latter type consumes 1/4 unit in 1hour.

Let the required consumption of coal be x units.

Less engines, Less coal consumed. (Direct Proportion)
More working hours, More coal consumed. (Direct Proportion).
Less rate of consumption, Less coal consumed. (Direct Proportion).

Number of engines   9 : 8
Working hours           8 : 13
Rate of consumption   1/3 : 1/4     :: 24 : x

[9 * 8 * (1/3) * x] = [8 * 13 * (1/4) * 24]
=> 24x = 624
=> x = 26.

Hence, the required consumption of coal = 26 metric tonnes.
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7.
A contract is to be cpmpleted in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?
Answer & Solution
Answer: d) 81

Solution:   Remaning work = [1 - (4/7)] = 3/7.

Remaining period = (46 - 33) days = 13 days.

Let the total men working at it be x.

Less work, Less men. (Direct Proportion)
Less days, More men. (Indirect Proportion)
More Hrs/Day, Less men. (Indirect Proportion).

Work         4/7 : 3/7
Days         13 : 22
Hrs/Day     9   :  8           :: 117 : x

(4/7) * 13 * 9 * x = (3/7) * 33 * 8 * 117
=> x = [(3 * 33 * 8 * 117) / (4 * 13 * 9)] = 198.

Additional men to be employed = (198 - 117) = 81.
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