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 ?

Answer: Option D

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