Question

A and B can do a piece of work in 21 and 24 days respectively. They start the work together, and after some days A leaves the work, and B completes the remaining work in 9 days. After how many days did A leave?

• A. 5
• B. 7
• C. 8
• D. 6

Hint:

Find what B alone did in the last 9 days first, then divide the rest by their combined daily rate.

Answer 1

The Correct Option is B

Working backward from B's final solo stretch is a clean way to isolate the joint working period.

1. Total work in convenient units: $\text{LCM}(21,24)=168$, giving A a rate of $8$ units/day and B a rate of $7$ units/day.
2. In B's last 9 days working alone, B completes $9 \times 7 = 63$ units.
3. So the joint work done before A left must be $168 - 63 = 105$ units.
4. Working together, A and B complete $8+7=15$ units per day, so the joint period lasted $\frac{105}{15}=7$ days.

So the correct answer is option B, 7 days.