Find A’s solo time from three pairwise times: A and B can do a job in 72 days, B and C in 120 days, and A and C in 90 days. How many days would A alone take to complete the work?

Introduction / Context: This mirrors the earlier pairwise method: sum the three pair rates to obtain twice the combined rate of all three. Then subtract the relevant pair to isolate the individual. The approach is algebraically neat and avoids a system of three unknowns directly.

Given Data / Assumptions:

• (A + B) = 1/72 work/day.
• (B + C) = 1/120 work/day.
• (A + C) = 1/90 work/day.

Concept / Approach: Sum: (A+B) + (B+C) + (A+C) = 2(A+B+C). Divide by 2 to get the combined rate of A, B, and C. Then A’s rate = (A+B+C) − (B+C). Invert to get A’s solo time in days.

Step-by-Step Solution:

Verification / Alternative check: Back-check: A = 1/120; then C = (A+C) − A = 1/90 − 1/120 = 1/360; and B = (A+B) − A = 1/72 − 1/120 = 1/180. Verify B + C = 1/180 + 1/360 = 1/120, correct.

Why Other Options Are Wrong: 60 or 90 days contradict the derived individual rates; 115 and 100 days are not supported by the rate sums given.

Common Pitfalls: Forgetting to halve the sum of pair rates; mixing up which pair to subtract to isolate A’s rate.

Final Answer: 120 days