A and B together can complete a piece of work in 12 days. A alone can complete the work in 15 days. In how many days can B alone complete the same work?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 60 days
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it each day, and the daily work of people working together adds up. So B’s daily work is the pair’s daily work minus A’s.
A and B together do \(\frac{1}{12}\) of the work a day; A alone does \(\frac{1}{15}\)
B alone: \(\displaystyle\frac{1}{12}-\frac{1}{15}=\frac{5-4}{60}=\frac{1}{60}\) of the work a day
So B alone needs 60 days
Shortcut:
When two people together take \(x\) days and one of them alone takes \(y\) days, the other alone takes \(\displaystyle\frac{xy}{y-x}\) days
\(\displaystyle\frac{12\times15}{15-12}=\frac{180}{3}=60\) days