Ratio between efficiency of A, B and R is 6 : 4 : 5. All three starts to work together with same efficiency. But R, destroys his 60% of work in every evening, due to which they have to work 20 more days than estimated time. Find the estimated days by them to complete the work.

Let total work = 1 unit, combined efficiency = 6+4+5=15 units/day. Estimated days = 1/15. With R's 60% evening destruction, net daily work = 15 - 60% of 5 = 12 units. Actual days = 1/12. Given actual = estimated + 20 days: 1/12 - 1/15 = 20. Solving: (5-4)/60 = 20, so 1/60 = 20, giving estimated days = 80. The key is recognizing that 20 extra days come from reduced net efficiency.