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

120 days

LCM method can be used, and the following chart is obtained:

Efficiency of A + B = 5, B + C = 3, A + C = 4

Adding all the efficiencies together

Thus 2(A + B + C) = 12, therefore, A + B + C = 6

If A + B + C = 6, and B + C = 3, then we can say efficiency of A = 3

Thus, total work = 360, efficiency of A = 3

Total days of A = \(\frac{ \text{Total work}}{\text{ Efficiency of A}}\)

Total days of A = \(\frac{ 360}{ 3}\)

Total days = 120