A and B can do a job in 72 days, B and C in 120 days, and A and C in 90 days. In how many days can A alone finish the job?

Introduction / Context:
With three workers and pairwise times, sum rates to get the combined rate, then back out individual rates. The target is the time for A alone.

Given Data / Assumptions:

• A + B: 72 days ⇒ 1/72
• B + C: 120 days ⇒ 1/120
• A + C: 90 days ⇒ 1/90

Concept / Approach:
Let a, b, c be daily rates. Then a + b + b + c + c + a = 2(a + b + c) equals the sum of given pair rates. Once a + b + c is known, use a + c and subtract c to solve for a, or use any pair.

Step-by-Step Solution:

Verification / Alternative check:
Plug a = 1/120 into A + B = 1/72 to get b, and into A + C = 1/90 to get c. The values are consistent with B + C = 1/120.

Why Other Options Are Wrong:
80, 100, 150, 90 do not satisfy all three pair equations when back substituted.

Common Pitfalls:
Arithmetic slips when summing reciprocals; forgetting to divide by 2 after adding pair rates; inconsistent rounding mid calculation.

Final Answer:
120 days