A and B can together complete a work in 8 days, B and C in 12 days, and C and A in 16 days. In how many days can C alone complete the work?

Solution

ATQ, Let daily work rates of A, B, C be a, b, c. a + b = 1/8 b + c = 1/12 c + a = 1/16 Add all: 2(a + b + c) = 1/8 + 1/12 + 1/16 LCM(8,12,16) = 48 1/8 = 6/48, 1/12 = 4/48, 1/16 = 3/48 Sum = 13/48 ⇒ a + b + c = 13/96 Now: a = (a + b + c) − (b + c) = 13/96 − 1/12 1/12 = 8/96 ⇒ a = (13 − 8)/96 = 5/96 ⇒ A alone: 96/5 = 19.2 days b = (a + b + c) − (c + a) = 13/96 − 1/16 1/16 = 6/96 ⇒ b = (13 − 6)/96 = 7/96 ⇒ B alone: 96/7 days c = (a + b + c) − (a + b) = 13/96 − 1/8 1/8 = 12/96 ⇒ c = (13 − 12)/96 = 1/96 ⇒ C alone: 96 days. Hence, C alone can complete work in 96 days