Twenty-four men can do a work in X days and 32 women can do the same work in (X + 8) days. The ratio of work done by 15 men and 12 women in the same time is 3:1. Find the value of X.

Correct answer: 10

Solution

Let one man's one-day work be m and one woman's one-day work be w. Given 15m : 12w = 3 : 1, so 15m = 36w and m = 12w/5. Total work by 24 men in X days equals total work by 32 women in X+8 days, so 24Xm = 32(X+8)w. Substituting m = 12w/5 gives X = 10.

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