Question

2 men and 7 boys can do a piece of work in 4 days the same work is done in 3 days by 4 men and 4 boys how long would it take one man and one boy to do it

Answer 1

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

According to the given condition,

2x + 7y = 1/4 (1)

and 4x + 4y = 1/3 (2)

Multiply equation (1) by 2 and subtract (2) from it, we get

4x + 14y - (4x + 4y) = 2/4 - 1/3

⇒ 10y = 1/2 - 1/3

⇒ 10y = 1/6

⇒ y = 1/60

On putting y in (2), we get

4x +4×1/60 = 1/3

⇒ 4x = 1/3 - 1/15

⇒ 4x = 4/15

⇒ x = 1/15

So, (1 man + 1 boy)'s 1 day's work = 1/15 + 1/60 = 1/12

Hence, 1 man and 1 boy together can finish the work in 12 days.