Correct Answer: (1)

Solution: (1) 24 men complete 1 work in 18 days.

What part of work will 27 men do in 8 days?

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

$\Rightarrow \frac{24 \times 18}{1}=\frac{27 \times 8}{W_{2}}$

$\Rightarrow W_{2}=\frac{27 \times 8}{24 \times 18}=\frac{1}{2}$

Remaining work $=1-\frac{1}{2}=\frac{1}{2}$

This part of work is to be done by 14 women.

$ \begin{aligned} & \therefore \frac{M_{1} D_{1}}{W_{1}}=\frac{M_{2} D_{2}}{W_{2}} \\ & \Rightarrow \frac{12 \times 28}{1}=\frac{14 \times D_{2}}{\frac{1}{2}} \\ & \Rightarrow 14 \times D_{2}=\frac{1}{2} \times 12 \times 28 \\ & \Rightarrow D_{2}=\frac{6 \times 28}{14}=12 \text { days } \end{aligned} $