A can complete a job in 20 days while B can complete it in 12 days. If B works alone for 9 days and then A completes the remaining work alone, how many days does A take to finish the remainder?

Introduction / Context:
This question mixes sequential work. We compute the fraction completed by B first, then the remaining fraction for A and divide by A’s rate to find the time required.

Given Data / Assumptions:

• A alone = 20 days ⇒ r(A) = 1/20 per day.
• B alone = 12 days ⇒ r(B) = 1/12 per day.
• B works for 9 days first.

Concept / Approach:
Completed by B = 9 * (1/12) = 3/4. Remaining = 1 − 3/4 = 1/4. A’s daily rate is 1/20, so time = (remaining) / r(A).

Step-by-Step Solution:
Work done by B: 9/12 = 3/4. Remaining work: 1/4. A’s time = (1/4) / (1/20) = 5 days.

Verification / Alternative check:
Total time = 9 + 5 = 14 days; combined output matches the full job (3/4 + 1/4).

Why Other Options Are Wrong:
3, 4, 7, 11 days do not match the exact remaining fraction and A’s rate.

Common Pitfalls:
Subtracting times rather than fractions of work; forgetting to compute the remaining fraction before dividing by A’s rate.

Final Answer:
5 days