15 men can finish a piece of work in 20 days, however it takes 24 women to finish it in 20 days. If 10 men and 8 women undertake to complete the work, then they will take ?

Answer: Option A

$$\begin{array}{rl}& \text{According to the question,}\\ & \text{15 men}=\text{20 days}\\ & \text{300 men}=1\text{ days}.....\text{(i)}\\ & \text{24 women}=\text{20 days}\\ & \text{480 men}=1\text{ days}......\text{(ii)}\\ & \text{Compare equation (i) and (ii)}\\ & \text{300 men}=480\text{ women}\\ & \text{5 men}=8\text{ women}.....\text{(iii)}\\ & \text{10 men}+8\text{ women}=?\\ & \text{10 men}+\text{5 men}=?\\ & 15\text{men}=?\end{array}$$
$$\text{15 men}\times \text{20 days}$$     = $$\text{15 men}$$  $$\times$$ $$x\text{ days}$$
$$x$$ = 20 days
Alternate
$$\begin{array}{rl}& \text{15m}\times \text{20 days}=24\text{w}\times 20\text{ days}\\ & \frac{\text{m}}{\text{w}}=\frac{8}{5}\end{array}$$
So, 1 man work 8 units work in one day
and 1 woman work 5 units work in one day
Total work = 15 × 8 × 20
Hence, (10 men + 8 women) work whole in D days
$$\begin{array}{rl}& \left(\text{10m}+\text{8w}\right)\times \text{D}=15\times 8\times 20\\ & \left(\text{10}\times \text{8}+\text{8}\times \text{5}\right)\times \text{D}=15\times 8\times 20\\ & \left(\text{80}+40\right)\times \text{D}=15\times 8\times 20\\ & \text{D}=20\text{ days}\end{array}$$