Question
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 can complete it in 20 days. How long will it take for A, B, and C to complete the work if all three work together?Solution
A+B = 12 days B+C = 15 days C+A = 20 days Let the total work has to be done by them = LCM of 12, 15, 20 = 300 A+B works in one day = 300/12 = 25 unit B+C works in one day = 300/15 = 20 unit C+A works in one day = 300/20 = 15 unit A+B+B+C+C+A = 25+20+15 = 60 unit A+B+C = 60/2 = 30 units Time taken to finish the work by A+B+C = 300/30 = 10 days
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