6 men can complete a work in 64 days while 24 women can complete the same work in 32 days. 16 men and 24 women together worked for 12 days, thereafter 8 men and 8 women left the work. In how many days the work completed?

15 days

Men × Days = Women × Days = Total Work

ATQ,

6 M × 64 = 24 W × 32

         1 M = 2 W

Efficiency ⇒ \(\frac{M}{W}\) = \(\frac{2}{1}\)

Total work ⇒ 6 M × 64 ⇒ (6 × 2) × 64 = 768

Now,

(16 M + 24 W) × 12 days work = {(16 × 2) + (24 × 1)} × 12 = 672

Remaining work = 768 - 672 = 96

After leaving by some person, this work is completed by 8 M and 16 W

So, Time taken by (8 M + 16 W) = \(\frac{96}{(8 × 2) + (16 × 1)}\) = \(\frac{96}{32}\) = 3 days

Therefore, Time taken for completing whole work = 12 + 3 = 15 days