B and C start; A finishes after they leave A can complete a job in 9 days, B in 10 days, and C in 15 days. B and C work together for 2 days and then leave. How long will A take to finish the remaining work?

Introduction / Context:
We first determine how much B and C accomplish together, then hand off to A for the remainder. Converting each time into a daily rate keeps the arithmetic straightforward.

Given Data / Assumptions:

• A: 9 days ⇒ 1/9 per day.
• B: 10 days ⇒ 1/10 per day.
• C: 15 days ⇒ 1/15 per day.
• B and C work 2 days, then stop.

Concept / Approach:
Combined rate(B+C) = 1/10 + 1/15 = 1/6 per day. Remainder = 1 − 2*(1/6). Then divide by A’s rate.

Step-by-Step Solution:

Verification / Alternative check:
In 6 days, A completes 6*(1/9) = 2/3, matching the remaining fraction.

Why Other Options Are Wrong:
9, 10, 13 contradict the exact fraction 2/3 at rate 1/9.

Common Pitfalls:
Adding 2 days to an option rather than recomputing with A’s solo rate.

Final Answer:
6 days