x women can complete a piece of work in 2y days. 1.5x men can complete the…
2019
x women can complete a piece of work in 2y days.
1.5x men can complete the same work in y days, while 2x children can complete it in 3y days.
8 women, 8 children and 8 men together can complete the same work in 22.5 days.
9 men can complete the same work in y + 20 days.
Solving the shared data gives x = 12 and y = 20.
If 36 women started the work and after 4 days 30 women are replaced by 8 men, find the total time in which the work will be completed.
- A.
20 ⁴⁄₂₅ days
- B.
22 ³⁄₂₅ days
- C.
12 days
- D.
12.5 days
- E.
24 ⁴⁄₂₅ days
Show answer & explanation
Correct answer: E
With x = 12 and y = 20, one woman-day rate is 1/480 and one man-day rate is 1/360. 36 women work for 4 days, completing 36 x 4/480 = 0.3 of the work. The remaining work is 0.7. After replacement, 6 women and 8 men work at 6/480 + 8/360 = 5/144 per day. Time for the remaining work is 0.7 divided by 5/144 = 20 4/25 days. Total time = 4 + 20 4/25 = 24 4/25 days.