Question
Ravi, Sohan, and Mohan can complete a certain task
individually in 18 days, 24 days, and 30 days, respectively. They all started working together, but after 6 days, Ravi and Mohan left, leaving Sohan to finish the remaining work alone. Determine the total number of days required to complete the entire task under these conditions.Solution
ATQ,Let total work be 360 units. {LCM (18, 24, and 30)}Efficiency of ‘Ravi’ = (360/18) = 20 units/dayEfficiency of ‘Sohan’ = (360/24) = 15 units/dayEfficiency of ‘Mohan’ = (360/30) = 12 units/dayWork completed in 6 days = {(20 + 15 + 12) × 6} = 282 unitsWork remaining = 360 – 282 = 78 unitsSo, time taken by ‘Sohan’ alone to complete the remaining work = {(360 – 282)/15} = 5.2 daysTherefore, total time taken to complete the work = (6 + 5.2) = 11.2 days
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