A and B can finish a job in 12 days, B and C in 15 days, and C and A in 20 days. How many days would A alone take to complete the job?

Introduction / Context:
With pairwise times, we can solve for individual rates. One reliable approach is to use the identity r(A) = [(A+B) + (A+C) − (B+C)] / 2 in rate form.

Given Data / Assumptions:

• r(A)+r(B) = 1/12.
• r(B)+r(C) = 1/15.
• r(C)+r(A) = 1/20.

Concept / Approach:
Use r(A) = [ (r(A)+r(B)) + (r(A)+r(C)) − (r(B)+r(C)) ] / 2 and then invert to get A’s time.

Step-by-Step Solution:
r(A) = [1/12 + 1/20 − 1/15] / 2. Compute with denominator 60: 1/12=5/60, 1/20=3/60, 1/15=4/60. Numerator = (5/60 + 3/60 − 4/60) = 4/60 = 1/15. Divide by 2 ⇒ r(A) = (1/15)/2 = 1/30 per day. Hence A’s time alone = 30 days.

Verification / Alternative check:
Sum of pairwise rates = 1/12 + 1/15 + 1/20 = 0.2; half is 0.1 ⇒ total rate of A+B+C = 1/10. Then B+C = 1/15 ⇒ A = 1/10 − 1/15 = 1/30 (consistent).

Why Other Options Are Wrong:
15 2/3, 24, 4, 20 days do not match the solved individual rate for A.

Common Pitfalls:
Forgetting to divide the adjusted sum by 2; mixing up which pair to subtract.

Final Answer:
30 days