A can do a piece of work in 12 days, while B alone can do it in 18 days. They work together for 6 days and the rest of the work is completed by C in 4 days. If they get Rs. 720 for the whole work, how should they divide the money?

A’s 1 day work = 1/12 B’s 1 day work = 1/18 (A + B) 1 day work = 1/12 + 1/18 = 3/36 + 2/36 = 5/36 Work done by A and B in 6 days = 6 × 5/36 = 5/6 Remaining work = 1 − 5/6 = 1/6 This remaining work is completed by C in 4 days. Now find individual shares of work: A’s work in 6 days = 6 × 1/12 = 1/2 B’s work in 6 days = 6 × 1/18 = 1/3 C’s work = 1/6 Ratio of work: A : B : C= 1/2 : 1/3 : 1/6 Taking LCM 6: = 3 : 2 : 1 Total ratio parts = 3 + 2 + 1= 6 Total money = Rs. 720 A’s share= 3/6 × 720= Rs. 360 B’s share = 2/6 × 720 = Rs. 240 C’s share = 1/6 × 720 = Rs. 120 Answer: A = Rs. 360 B = Rs. 240 C = Rs. 120