A and B together can complete a job in 15 days. B alone can complete it in 20 days. In how many days can A alone complete the job?

Introduction / Context: When you know the combined time and one individual’s time, you can find the other’s rate by subtracting rates, then invert to find the time for the other individual alone.

Given Data / Assumptions:

• A + B = 15 days.
• B alone = 20 days.
• Rates are constant and additive.

Concept / Approach: Convert times to rates: r(A+B) = 1/15; r(B) = 1/20. Then r(A) = r(A+B) − r(B). Finally, A’s time = 1 / r(A).

Step-by-Step Solution: r(A+B) = 1/15 per day. r(B) = 1/20 per day. r(A) = 1/15 − 1/20 = (4 − 3)/60 = 1/60. A’s time = 1 / (1/60) = 60 days.

Verification / Alternative check: Check: 1/60 + 1/20 = 1/60 + 3/60 = 4/60 = 1/15. Correct.

Why Other Options Are Wrong: 30, 35, 40, 45 days do not satisfy the rate equations with the given combined time of 15 days.

Common Pitfalls: Averaging days directly; forgetting that rates (not times) add.

Final Answer: 60 days