A man and a boy can do a piece of work in 24 days. If the man works alone for the last 6 days, it is completed in 26 days. How long would the boy take to do it alone ?

Solution (By Examveda Team)

(M + B)'s 1 day's work =$$\frac{1}{{24}}$$
(M + B)'s 20 day's work + M's 6 day's work = 1
$$\eqalign{ & \Rightarrow {\text{M's 6 day's work}} \cr & = \left( {1 - \frac{1}{{24}} \times 20} \right) \cr & = \frac{4}{{24}} = \frac{1}{6} \cr & \Rightarrow {\text{M's 1 day's work}} \cr & = \frac{1}{6} \times \frac{1}{6} \cr & = \frac{1}{{36}} \cr & \therefore {\text{B's 1 day's work}} \cr & = \frac{1}{{24}} - \frac{1}{{36}} \cr & = \frac{1}{{72}} \cr} $$
Hence, the boy alone can do the work in 72 days.