A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C and do it in 90 days. In what time can A alone do it?

(A + B )'s 1 day ' s work = 1/72
(B + c)'s 1 day' s work = 1/120
(A + C)'s 1 day's work = 1/90
2(A + B + C)'s 1 days work = 1/72 + 1/120 + 1/90
∴ ( A + B + C )'s 1 day's work (5 + 3 + 4)/(360 x 2) = 12/(360 x 2) = 1/60
∴ A's 1 day's work = (A + B + C) 's 1 day's work - (B + C)'s 1 day's work
= 1/60 - 1/120 = (2 - 1)/120 = 1/120
∴ A alone can finish the work in 120 days.