A and B working together can finish a piece of work in 12 days while B alone can finish the same work in 30 days. Then determine that in how many days can A alone finish the same work?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20 days
A person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and one-day works add up when people work together. So A’s one-day work is the joint one-day work minus B’s.
A and B together: \(\frac{1}{12}\) of the work a day
B alone: \(\frac{1}{30}\) of the work a day
A alone: \(\displaystyle \frac{1}{12}-\frac{1}{30}=\frac{5-2}{60}=\frac{3}{60}=\frac{1}{20}\) of the work a day
So A alone finishes the work in 20 days