A and B together take 18 days to finish a job, B and C take 24 days, and C and A take 36 days. In how many days can A, B, and C together finish the job?

Introduction / Context:When pairwise completion times are given, we can derive individual rates and then sum them to get the combined time.

Given Data / Assumptions:

• (A + B) time = 18 days ⇒ rate = 1/18
• (B + C) time = 24 days ⇒ rate = 1/24
• (C + A) time = 36 days ⇒ rate = 1/36

Concept / Approach:Let a, b, c be daily rates. Then a + b = 1/18, b + c = 1/24, c + a = 1/36. Add all three to eliminate pairs and solve for a + b + c.

Step-by-Step Solution:

Verification / Alternative check:Individual rates computed from pair sums are consistent, but the problem only requires the total sum, which we obtained directly.

Why Other Options Are Wrong:8, 24, 36, 12 come from misadding reciprocals or forgetting to divide the pairwise sum by 2 to get the triple sum.

Common Pitfalls:Adding times instead of rates; not halving the total of pair rates; arithmetic mistakes with fractions 1/18, 1/24, 1/36.

Final Answer:16