Correct Answer: (4)

Solution: (4)

8 men can do 1 work in 25 days.

15 women can do the same work in 16 days.

$\therefore(8 \times 25)$ men $=(15 \times 16)$ women

$\therefore 5$ men $= 6$ women

$\therefore 4$ men +8 women $=\left(4+\frac{5}{6} \times 8\right)$ men $=\left(4+\frac{20}{3}\right)$ men $= \frac{32}{3}$ men

$\because \frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}}$

$\Rightarrow \frac{8 \times 25}{1}=\frac{\frac{32}{3}}{W_{2}} \times 10$

$\Rightarrow W_{2}=\frac{32 \times 10}{3 \times 8 \times 25}=\frac{8}{15}$

Remaining work $=1-\frac{8}{15}=\frac{7}{15}$

Again, 6 men join the team.

$\therefore$ Number of men $=\frac{32}{3}+6$ $=\frac{50}{3}$

$\therefore \frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}}$

$\Rightarrow \frac{8 \times 25}{1}=\frac{\frac{50}{3} \times D_{2}}{\frac{7}{15}}$

$\Rightarrow 8 \times 25=\frac{50}{3} \times \frac{15}{7} \times D_{2}$

$\Rightarrow D_{2}=\frac{8 \times 25 \times 7}{50 \times 5}=\frac{28}{5}$ $=5 \frac{3}{5}$ days