If 3 men or 9 boys can finish a piece of work in 21 days, in how many days can 5 men and 6 boys together do the same piece of work ?

Answer: Option E

$$\begin{array}{rl}& \text{1 men’s 1 day’s work}\\ & =\frac{1}{21\times 3}\\ & =\frac{1}{63}\\ & \text{1 boy’s 1 day’s work}\\ & =\frac{1}{21\times 9}\\ & =\frac{1}{189}\\ & \left(\text{5 men}+\text{6 boy}\right)\text{’s 1 day’s work}\\ & =\frac{5}{63}+\frac{6}{189}\\ & =\frac{5}{63}+\frac{2}{63}\\ & =\frac{7}{63}\\ & =\frac{1}{9}\end{array}$$
Hence, 5 men's and 6 boy's together can do the work in 9 days.