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 ?

Solution(By Examveda Team)

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,
$$\eqalign{ & \Rightarrow \frac{1}{{5x}} + \frac{1}{{8x}} = \frac{1}{{40}} \cr & \Rightarrow \frac{{13}}{{40x}} = \frac{1}{{40}} \cr & \Rightarrow x = 13 \cr} $$
Hence, time taken by the boy to complete the work alone
$$\eqalign{ & {\text{ = }}\left( {8 \times 13} \right){\text{days}} \cr & {\text{ = 104 days}} \cr} $$