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

Step 1: Set the total work.
Let total work \(=\text{LCM}(21,24)=168\) units.

Step 2: Find individual daily rates.
A's rate \(=\dfrac{168}{21}=8\) units/day. B's rate \(=\dfrac{168}{24}=7\) units/day.

Step 3: Set up the equation.
Let A and B work together for p days, doing \((8+7)p=15p\) units. The remaining work, \(168-15p\), is finished by B alone in 9 days at 7 units/day, so \(168-15p=7\times9=63\).

Step 4: Solve for p.
\(15p=168-63=105 \Rightarrow p=7\).

Step 5: Final Answer.
A left after 7 days, so option B is correct.