A man and a boy together can do a certain amount of digging in 24 days. Their speeds in digging are in the ratio of 4 : 3. How many days will the boy take to complete the work if engaged alone?

56 days

Man + Boy = 24 days,

⇒ M : B = 4 : 3   (Efficiency)

⇒ Total work = (4 + 3) x 24 = 7 x 24 = 168 units,   ..(Efficiency × Days = Total work)

⇒ Time required by Boy to complete the work alone = \(\frac{168}{3}\) = 56 days,    ..(\(\frac{Work}{Efficiency}\) = Time)