Three men and four women can do a piece of work in 7 days, whereas 2 men and 1 women can do it in 14 days. 07 women will complete the same work in:

10

Total Work = (3M + 4W) × 7   .....(i)

Total Work = (2M + 1W) × 14 .....(ii)

ATQ, Total work is same, then

(3M + 4W) × 7 = (2M + 1W) × 14

3M + 4W = (2M + 1W) × 2

3M + 4W = 4M + 2W

1M = 2W

⇒ M : W = 2 : 1

From (i),

Total work = (6 + 4) × 7 = 70

⇒ Efficiency of 7 women = 7 × 1 = 7

Therefore,

7 women will do the work in = \(\frac{70}{7}\)= 10 days