A and B together can finish a job in 8 days, B and C together in 9 days, and C and A together in 24 days. In how many days can A alone finish the job?

Add the three pair-rates: 2(A + B + C) = 1/8 + 1/9 + 1/24 = (9 + 8 + 3)/72 = 20/72 = 5/18.

So A + B + C = 5/36 of the job per day.

A = (A + B + C) − (B + C) = 5/36 − 1/9 = 5/36 − 4/36 = 1/36 → A alone takes 36 days.

Tip: take the job as LCM(8, 9, 24) = 72 units: pair-rates 9, 8, 3 → total 20 → combined 10 units/day → A = 10 − 8 = 2 units/day → 36 days.