Question
Time taken by 'A', 'B' and 'C' to complete a work is 51
days, 85 days and 102 days respectively. All of them started the work together but 'B' and 'A' left the work 19 days and 9 days respectively before the completion of work. Find the total time taken to complete the work.Solution
Let the total work be 510 units (LCM of 51, 85 and 102) Efficiency of 'A' = (510/51) = 10 units/day Efficiency of 'B' = (510/85) = 6 units/day Efficiency of 'C' = (510/102) = 5 units/day Let the time taken to complete the work be 'n' days. So, (10 + 6 + 5) X (n - 19) + (10 + 5) X 10 + 5 X 9 = 510 Or, 21n - 399 + 150 + 45 = 510 Or, 21n = 714 Or, 'n' = 34
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