Pairwise Work Times Given — Find C Alone A and B can do a job in 12 days, B and C in 15 days, and C and A in 20 days. How many days will C alone take to complete the job?

Introduction / Context:
Given three pairwise completion times, we can find the sum of individual rates and then isolate the rate for a single worker by subtracting an appropriate pair rate. This is a classic system-of-rates problem.

Given Data / Assumptions:

• (A + B) time = 12 ⇒ rate = 1/12.
• (B + C) time = 15 ⇒ rate = 1/15.
• (C + A) time = 20 ⇒ rate = 1/20.

Concept / Approach:
Sum: 2(A + B + C) rate = 1/12 + 1/15 + 1/20. Then (A + B + C) rate = half of that. C's rate = (A + B + C) − (A + B).

Step-by-Step Solution:
1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 12/60 = 1/5.(A + B + C) rate = (1/5)/2 = 1/10.C's rate = 1/10 − 1/12 = (6 − 5)/60 = 1/60.C alone time = 60 days.

Verification / Alternative check:
Compute A and B similarly if desired; all rates are consistent.

Why Other Options Are Wrong:
Any time other than 60 contradicts the derived rate 1/60.

Common Pitfalls:
Forgetting to divide by 2 after summing the three pairwise rates.

Final Answer:
60