Question

A man and a boy can do a piece of work in 24 days. If the man works alone for last 4 days, it is complete in 5 days. How long would the boy take to do it alone?

• A. 120 days
• B. 20 days
• C. 80 days
• D. 36 days

Answer 1

The correct option is A 120 days

(Man + boy)'s one day's work $=\frac{1}{24}$
(Man + boy)'s 20 day's work $=\frac{20}{24}=\frac{5}{6}$
Remaining $\frac{1}{6}$ of the work is done by the man alone in 5 days, i.e., the man alone can do $\frac{1}{30}$ of the work in 1 day.
$\therefore$ Boy's one day's work $=\frac{1}{24}-\frac{1}{30}=\frac{1}{120}$.
$\therefore$ Boy alone would take 120 days to complete the work.