A man and a boy together can do a certain amount of digging in 40 days. Their speeds in digging are in the ratio of 8 : 5. How many days will the boy take to complete the work if engaged alone ?

Answer: Option D

Ratio of digging speeds of man and boy = 8 : 5
Ratio of times taken by man and boy = 5 : 8
Suppose the man takes 5x days while the takes 8x
Then,
$$\begin{array}{rl}& \Rightarrow \frac{1}{5x}+\frac{1}{8x}=\frac{1}{40}\\ & \Rightarrow \frac{13}{40x}=\frac{1}{40}\\ & \Rightarrow x=13\end{array}$$
Hence, time taken by the boy to complete the work alone
$$\begin{array}{rl}& \text{ = }\left(8\times 13\right)\text{days}\\ & \text{ = 104 days}\end{array}$$