Question
Rahul, Rohit, and Raj alone can complete a project in
40, 80, and 120 days respectively. All of them started working together, but after 10 days, Rahul left the job, and 12 more days later, Rohit also left the job. So for how many days did Raj work?Solution
 Total work = LCM of 40, 80, and 120 = 240 units.  Rahul's daily work = 240/40 = 6 units.  Rohit's daily work = 240/80 = 3 units.  Raj's daily work = 240/120 = 2 units.  Work done in the first 10 days = 10 × (6 + 3 + 2) = 110 units.  Work done by Rohit and Raj together in the next 12 days = 12 × (3 + 2) = 60 units.  Remaining work = 240 - 110 - 60 = 70 units.  Time taken by Raj alone to complete the remaining work = 70/2 = 35 days.  Total days Raj worked = 10 + 12 + 35 = 57 days
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