A and B together can finish a work in 8 days. If A alone can finish it in 12 days, then how many days will B alone need to finish the work?

Introduction / Context: With the combined time and one individual’s time available, we subtract rates to find the other individual’s time. This is a standard rate subtraction technique.

Given Data / Assumptions:

• A + B = 8 days ⇒ r(A+B) = 1/8 per day.
• A alone = 12 days ⇒ r(A) = 1/12 per day.

Concept / Approach: r(B) = r(A+B) − r(A) = 1/8 − 1/12. Then B’s time = 1 / r(B).

Step-by-Step Solution: 1/8 − 1/12 = (3 − 2)/24 = 1/24. Therefore, B’s time = 1 / (1/24) = 24 days.

Verification / Alternative check: 1/12 + 1/24 = 1/8; hence A and B together take 8 days as given.

Why Other Options Are Wrong: 12, 18, 20, 28 days do not produce the given combined time when paired with A’s 12-day rate.

Common Pitfalls: Adding times instead of rates; miscomputing the common denominator when subtracting fractions.

Final Answer: 24 days