'Q' is 20% less efficient than 'P' and 'R' is 60% more efficient than 'P'. If 'Q' takes 20 more days than 'R' to complete the same work, then find the time taken by 'P' to complete this work.

ATQ, Let the efficiency of 'P' be '10x' units/day So, efficiency of 'Q' = 10x X 0.80 = '8x' units/day And efficiency of 'R' = 10x X 1.6 = '16x' units/day So, ratio of efficiency of 'Q' and 'R' = 8x:16x = 1:2 So, ratio of time taken by 'Q' and 'R' to finish the same work = 2:1 (efficiency is inversely proportional to the time taken) Let the time taken by 'Q' to do this work be '2y' days So, time taken by 'R' = 2y X (1/2) = 'y' days So, 2y - y = 20 Or, y = 20 So, time taken by 'Q' to finish the work = 20 X 2 = 40 days Now, ratio of efficiency of 'P' and 'Q' = 10x:8x = 5:4 So, ratio of time taken by 'P' and 'Q' to finish the same work = 4:5 So, time taken by 'P' to finish the work = 40 X (4/5) = 32 days