Ram and Rajan complete a project in 3 days. Mohan and Rohan complete the same project in 3 days. Rajan is 50% more efficient than Mohan and Rohan completes the project in 6 days. What is the ratio of time taken by Ram and Rohan together to the time taken by Mohan and Rajan together ?

Let total work = 1 unit. Rohan alone completes in 6 days, so Rohan's rate = 1/6 per day. Rajan is 50% more efficient than Mohan, so Rajan = 1.5 × Mohan. Ram + Rajan = 1/3 (complete in 3 days), Mohan + Rohan = 1/3. From Mohan + Rohan = 1/3 and Rohan = 1/6, we get Mohan = 1/3 - 1/6 = 1/6. So Rajan = 1.5 × 1/6 = 1/4. From Ram + Rajan = 1/3, Ram = 1/3 - 1/4 = 1/12. Time(Ram + Rohan) = 1/(1/12 + 1/6) = 1/(1/12 + 2/12) = 1/(3/12) = 4 days. Time(Mohan + Rajan) = 1/(1/6 + 1/4) = 1/(2/12 + 3/12) = 1/(5/12) = 12/5 = 2.4 days. Ratio = 4:2.4 = 5:3.