A and B can do a piece of work in 45 days and 40 days, respectively. They start together, but A leaves after some days. B then completes the remaining work alone in 23 days. After how many days from the start did A leave?

Introduction / Context:
We split the timeline into two phases: joint work for x days and then B alone for 23 days. Using constant daily rates simplifies the calculation.

Given Data / Assumptions:

• A’s rate = 1/45 job/day.
• B’s rate = 1/40 job/day.
• Joint work for x days; B alone for 23 days; total work = 1 job.

Concept / Approach:
Write the work sum: x*(1/45 + 1/40) + 23*(1/40) = 1. Solve for x.

Step-by-Step Solution:

Verification / Alternative check:
Compute total: 9*(17/360) + 23/40 = 153/360 + 207/360 = 360/360 = 1 job; exact.

Why Other Options Are Wrong:
7, 8, 10, 11 days would not satisfy the exact rate equation.

Common Pitfalls:
Rounding fractions too early; mixing up who worked when.

Final Answer:
9 days