Question

Two men and three boys together can do a piece of work in 8 days. The same work is done in 6 days by 3 men and 2 boys together. How long would 1 boy alone or 1 man alone take to complete the work?

(a) 1 man alone: 24 days, 1 boy alone: 36 days
(b) 1 man alone: 32 days, 1 boy alone: 48 days
(c) 1 man alone: 36 days, 1 boy alone: 54 days
(d) 1 man alone: 48 days, 1 boy alone: 72 days

Answer 1

It would take one man alone 24 days to complete the work, and it would take one boy alone 36 days to complete the work.

Step-by-step explanation:

Let's assume that the amount of work done in 1 day by a man is 'm' and the amount of work done in 1 day by a boy is 'b'.

From the given information, we can form two equations:

Equation 1: 2m + 3b = 1/8 (since two men and three boys can finish the work in 8 days)

Equation 2: 3m + 2b = 1/6 (since three men and two boys can finish the work in 6 days)

Solving these equations simultaneously, we find that m = 1/12 and b = 1/24.

Therefore, it would take one man alone 24 days to complete the work, and it would take one boy alone 36 days to complete the work.