3 men and 5 women can do a work in 14 days while 5 men can do it in 14 days. 5 men and 5 women can complete the work in 3

According to the question,

(3M + 5W) × 14 = 5M × 14

5 W = 2M

$\frac{\mathrm{W}}{\mathrm{M}}=\frac{2}{5}$

Total work = 5 × 5 × 14 = 25 × 14

Time taken to complete the work by 5 men and 7 women

$=\frac{25 \times 14}{5 \times 5+5 \times 2}=\frac{25 \times 14}{35}=10$ days