Separating individual time from combined time: A and B together can complete a work in 35 days, while A alone can do it in 60 days. In how many days will B alone complete the same work?

Introduction / Context: This is a standard decomposition: with A’s solo time and the team time known, we can compute B’s solo rate by subtracting A’s rate from the joint rate. The solo time for B is then the reciprocal of that rate. Keep all rates in work/day for consistency.

Given Data / Assumptions:

• (A + B) time = 35 days ⇒ rate(A+B) = 1/35.
• A time = 60 days ⇒ rate(A) = 1/60.
• Job size = 1 unit of work.

Concept / Approach: rate(B) = rate(A+B) − rate(A) = 1/35 − 1/60. Find a common denominator and compute. Then time(B) = 1 / rate(B).

Step-by-Step Solution:

Verification / Alternative check: Check the combined rate: 1/60 + 1/84 = (7 + 5)/420 = 12/420 = 1/35, matching the given team time.

Why Other Options Are Wrong: 80, 88, 92, and 72 days do not satisfy the exact rate subtraction and will not reconstruct the 35-day joint time when combined with A’s rate.

Common Pitfalls: Subtracting times instead of rates, or using incorrect denominators when combining fractions.

Final Answer: 84 days