Question

A and B together need to complete a piece of work in 15 days. They both start working together, but after 6 days B falls ill, so A takes 30 more days to complete the work alone. How long will B take to complete the work alone?

• A. 23 days
• B. 20 days
• C. 26 days
• D. 21 days

Answer 1

The correct option is D

21 days

(A+B)'s 1-day work = $\frac{1}{15}$
(A+B)'s 6-day work = $\frac{6}{15}$
Remaining work = 1 - $\frac{6}{15}$ = $\frac{9}{15}$ = $\frac{3}{5}$
A takes 30 days to complete remaining work.
A's 1-day work = $\frac{\frac{3}{5}}{30}$ = $\frac{1}{50}$
So, A takes 50 days to complete full work alone.
B's 1-day work = $\frac{1}{15}$ - $\frac{1}{50}$ = $\frac{7}{150}$
B takes $\frac{150}{7}$ or 21.4 or 21 days (approx.)