A and B can complete a work in 10 hours, B and C in 15 hours, and A and C in 12 hours. How long will B alone take to complete the work?

Introduction / Context:Pairwise completion information allows us to compute the sum of individual hourly rates and then isolate any one worker’s rate by subtraction.

Given Data / Assumptions:

• A + B: 10 h ⇒ 1/10 per hour.
• B + C: 15 h ⇒ 1/15 per hour.
• A + C: 12 h ⇒ 1/12 per hour.

Concept / Approach:Let a, b, c be hourly rates. Then a + b = 1/10, b + c = 1/15, a + c = 1/12. Sum to get 2(a + b + c), divide by 2 for the total rate, then subtract (a + c) to get b.

Step-by-Step Solution:

Verification / Alternative check:Compute a and c similarly and verify that the pair sums equal the given rates. The arithmetic is consistent.

Why Other Options Are Wrong:12 h, 16 h, 20 h, 18 h do not match the extracted b when recombined into pair rates.

Common Pitfalls:Adding hours instead of rates; forgetting to divide the pair sum by 2; sign mistakes while subtracting to isolate b.

Final Answer:24 h