Question

2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

Answer 1

Let the work completed by 1 man in a day be m and that by a woman be w

Then 2w + 5m = work completed by 2 women and 5 men in a day

Since they take 4 days to complete, in one day they complete $\frac{1}{4}$ of the work

Hence 2w + 5m = $\frac{1}{4}$

Similarly,

3w + 6m = $\frac{1}{3}$

On solving, we get m = $\frac{1}{36}$, w = $\frac{1}{18}$