A and B together can complete a work in 12 days. B and C together can complete the same work in 15 days, and A and C together in 20 days. If they all work together and earn Rs 7,200 for the whole work, find B’s share of the money.

Solution

ATQ, Let daily work rates of A, B, C be a, b, c. Given: a + b = 1/12 …(1) b + c = 1/15 …(2) a + c = 1/20 …(3) Add all: 2(a + b + c) = 1/12 + 1/15 + 1/20 LCM of 12, 15, 20 is 60. 1/12 = 5/60, 1/15 = 4/60, 1/20 = 3/60 Sum = 12/60 = 1/5 So a + b + c = 1/10 (whole work done in 10 days by all three) Now find b: b = (a + b + c) − (a + c) = 1/10 − 1/20 = (2 − 1)/20 = 1/20 So B’s 1-day work = 1/20 Total daily work = 1/10 Share of B in work = (1/20) ÷ (1/10) = 1/2 So B’s share of Rs 7,200 = 1/2 × 7200 = Rs 3,600