Kusum, Joy and Mona together can complete a piece of work in (y-18) days. The efficiency of Kusum is 62.5% less than the efficiency of Mona. Joy alone can do the same piece of work in 120 days. The efficiency of Kusum is 25% less than the efficiency of Joy. Find out the time taken by Kusum alone to complete the same piece of work alone.

Let’s assume the total work is 480 units. Joy alone can do the same piece of work in 120 days. Efficiency of Joy = 480/120 = 4 units/day The efficiency of Kusum is 25% less than the efficiency of Joy. efficiency of Kusum = (100-25)% of 4 = 75% of 4 = 3 units/day The efficiency of Kusum is 62.5% less than the efficiency of Mona. 3 = (100-62.5)% of efficiency of Mona 3 = 37.5% of efficiency of Mona 3 = 0.375 x (efficiency of Mona) efficiency of Mona = 8 units/day Kusum, Joy and Mona together can complete a piece of work in (y-18) days. (3+4+8)x(y-18) = 480 15x(y-18) = 480 (y-18) = 32 y = 32+18 y = 50 Time taken by Kusum alone to complete the same piece of work alone = 480/3 = 160 days = (3y+10) days