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

120 days

Total work = LCM of 72, 120 and 90

Total work = 360 units

Efficiency of A and B = 360/72 = 5 unit

Efficiency of B and C = 360/120 = 3 unit

Efficiency of A and C = 360/90 = 4 unit

Efficiency of A, B and C

⇒ (5 + 3 + 4)/2

⇒ 6 units

A + B + C = 6 units

Efficiency of A = 6 units - efficiency of (B + C)

Efficiency of A = (6 - 3) = 3 units

A alone can complete the work 

⇒ 360/3 = 120 days.