Rahul alone can do 60% of the same piece of work in (z-4) days. Queen and Rahul together can do 75% of the same piece of work in (0.5z+4) days. Pankaj alone can do the same piece of work in 45 days. The efficiency of Rahul is 12.5% more than the efficiency of Pankaj. If the efficiency of Queen is ‘y’% less than that of Pankaj, then find out the value of ‘z’ is what percentage of the value of ‘y’.

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%