6 men can do a piece of work in 12 days while 8 women can do the same work in 18 days. The same work can be done by 18 children in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men have to complete remaining work in 1 day, then find the required number of men?
A
Correct answer
Explanation
6 men in 12 days means 1 man does 1/72 of work per day. 8 women in 18 days means 1 woman does 1/144 of work per day. 18 children in 10 days means 1 child does 1/180 of work per day. Work done by 4 men + 12 women + 20 children in 2 days = 2×(4/72 + 12/144 + 20/180) = 2×(1/18 + 1/12 + 1/9) = 2×(2/36 + 3/36 + 4/36) = 2×(9/36) = 1/2. Remaining work = 1/2. If men complete this in 1 day, we need m men such that m/72 = 1/2, so m = 36 men are required.