30 men can do a work in X days and 25 women can do same work in (X+9) days. If the amount of work done by 36 men in 3 days is equal to the work done by 90 women in 2 days. Find in how many days 15 men and 5 women can do the work?

Let the total work be W. From the given: 30 men do W work in X days, so 1 man's 1 day work = W/(30X). Similarly, 25 women do W work in (X+9) days, so 1 woman's 1 day work = W/[25(X+9)]. The condition '36 men in 3 days = 90 women in 2 days' gives: 36 × 3 × W/(30X) = 90 × 2 × W/[25(X+9)]. Solving: 108/(30X) = 180/[25(X+9)], which simplifies to X = 9. Therefore, 1 man's rate = 1/270 and 1 woman's rate = 1/450. For 15 men and 5 women: combined rate = 15/270 + 5/450 = 1/18 + 1/90 = 6/90 = 1/15. So they complete the work in 15 days.