12 men can do a piece of work in 15 days and 20 women can do the same work in 12 days. In how many days can 5 men and 5 women complete the same work ?

Answer: Option A

12 man × 15 = 20 women × 12 = Total work
3 man = 4 women
$$\begin{array}{rl}& \frac{\text{Men}}{\text{Women}}=\frac{4}{3}\to \text{Efficiency}\\ & \text{Total work}=12\times 4\times 15=720\\ & \left(5\text{ man}+5\text{ women}\right)\times \text{D}=720\\ & \text{D}\left(5\times 4+5\times 3\right)=720\\ & \text{D}=\frac{720}{35}=20\frac{4}{7}\text{ days}\end{array}$$

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Alternate:
According to the question,
12 men can do the 1 day work in $$\frac{1}{15}$$ days
So, 1 men can do the 1 day work in $$\frac{1}{15\times 12}$$  = $$\frac{1}{180}$$ days
5 men can do the 1 day work in $$\frac{1}{180}\times 5$$   = $$\frac{5}{180}$$ days
Similarly 5 women do the 1 dys work $$\frac{5}{240}$$ days
∴ 5 men & 5 women together work in 1 day
$$\begin{array}{rl}& =\frac{5}{180}+\frac{5}{240}\\ & =\frac{20+15}{720}\\ & =\frac{35}{720}\end{array}$$
Hence, they complete the work $$\frac{720}{35}$$ = $$20\frac{4}{35}$$ days