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Question

In 25 days, one-fifth work is done by 10 men. If the number of days taken to complete three-fifth of the work is 75 days, then how many men were engaged?

A
11 men
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B
12 men
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C
10 men
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D
8 men
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Solution

The correct option is C 10 men
Here, the number of days is inversely proportional to the number of men and directly proportional to the amount of work done.
Number of days Amount of work done Number of men
25 15 10
75 35 x
25 : 75 =
1 : 3
15:35 10 : x

Number of men 1Number of days
10 : x = 3 : 1 ...(i)

Amount of work Number of men
15 : 35 = 10 : x ...(ii)

From (i) and (ii)
10 : x
=compound ratio of 3 : 1 and 15 : 35
10 : x = (3 : 1) × (15 : 35)
10 : x = (3 × 15) : (1 × 35)
10 : x = (35 : 35)

Product of means = Product of extremes
x × 35 = 10 × 35
x = 10

So, ten men were engaged.

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