Solution

Let’s assume the total work is 360 units. Pankaj alone can do the same piece of work in 45 days. Efficiency of Pankaj = 360/45 = 8 units/day The efficiency of Rahul is 12.5% more than the efficiency of Pankaj. Efficiency of Rahul = (100+12.5)% of 8 = 112.5% of 8 = (112.5x8)/100 = 9 units/day Rahul alone can do 60% of the same piece of work in (z-4) days. Time taken by Rahul alone to complete the work alone = [(z-4)/60]x100 = [(z-4)/3]x5 So [[(z-4)/3]x5]x9 = 360 [(z-4)/3]x5 = 40 [(z-4)/3] = 8 (z-4) = 24 z = 24+4 z = 28 Queen and Rahul together can do 75% of the same piece of work in (0.5z+4) days. Time taken by Queen and Rahul together to complete the whole work = [(0.5z+4)/75]x100 = [(0.5z+4)/3]x4 (Efficiency of Queen + 9)x[(0.5z+4)/3]x4 = 360 Put the value of ‘z’ in the above equation. (Efficiency of Queen + 9)x[(0.5x28+4)/3]x4 = 360 (Efficiency of Queen + 9)x[(14+4)/3]x4 = 360 (Efficiency of Queen + 9)x[18/3]x4 = 360 (Efficiency of Queen + 9)x6x4 = 360 (Efficiency of Queen + 9)x24 = 360 (Efficiency of Queen + 9) = 15 Efficiency of Queen = 15-9 = 6 If the efficiency of Queen is ‘y’% less than that of Pankaj. 6 = (100-y)% of 8 6 = [(100-y) x 8]/100 3 = [(100-y) x 4]/100 300 = (400-4y) 4y = 400-300 4y = 100 y = 25 Required percentage = (z/y)x100 = (28/25)x100 = 28x4 = 112%