'Q' is 20% less efficient than 'P' and 'R' is 60% more

Solution

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