Correct Answer: (2)

Solution: (2) According to the question,

$18 \times 16$ women $\equiv 24 \times 18$ children

$\Rightarrow 2$ women $\equiv 3$ children

$\therefore 8$ women +16 children $=(12+16)$ children $=28$ Children

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

$\Rightarrow \frac{24 \times 18}{1}=\frac{28 \times 9}{W_{2}}$

$\Rightarrow W_{2}=\frac{28 \times 9}{24 \times 18}=\frac{7}{12}$

$\therefore$ Remaining work $=1-\frac{7}{12}=\frac{5}{12}$

This part of work is done by 10 men.

$\frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}}$ $\Rightarrow \frac{12 \times 20}{1}=\frac{10 \times D_{2}}{\frac{5}{12}}$

$\Rightarrow 10 \times D_{2}=12 \times 20 \times \frac{5}{12}$ $=100$

$\Rightarrow D_{2}=\frac{100}{10}=10$ days