Question 17

4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women finish it?

Solution

Let the amount of work done by each men per each day be X.
Let the amount of work done by each women per each day be Y.
Let the total amount of work be W.

Given 4 men & 6 women finish job in 8 days : (4X + 6Y)(8) = W
Given 3 men and 7 women finish job in 10 days : (3X + 7Y)(10) = W

Upon solving above two equations, we get : X = 11 Y
Substituting the same in (4X + 6Y)(8) = W
(44Y + 6Y)(8) = W
Y = W/400

Therefore, if only 10 women work on this job : 10Y(t) = W
Hence, t = 40 days.

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