Question
Pawan, Bittu, and Raju can individually complete a task
in 36 days, 60 days, and 30 days, respectively. They all begin working together, but Raju stops after 5 days. Additionally, Pawan leaves the work 18 days before its completion. How many days does it take to complete the entire task?Solution
Let the total work = 180 units (LCM of 36, 60 and 30) Amount of work done by Pawan alone in one day = 180/36 = 5 units Amount of work done by Bittu alone in one day = 180/60 = 3 units Amount of work done by Raju alone in one day = 180/30 = 6 units Amount of work done by Pawan, Bittu and Raju together in 5 days = 5 × (5 + 3 + 6) = 70 units Amount of work done by Bittu alone in 18 days = 18 × 3 = 54 units Remaining work = 180 – 70 – 54 = 56 units Time taken by Pawan and Bittu together to complete 56 units work = 56/(5 + 3) = 7 days So the total time taken to complete the work = 5 + 18 + 7 = 30 days
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