'X' and 'Y' can complete a certain job together in 36 days. They worked together for 20 days, after which 'X' left, and 'Y' completed the remaining work alone in 40 days. Determine the amount of time it would take for 'Y' to finish the entire job if he worked on it alone from the start.

Solution

Let the efficiency of 'X' and 'Y' be 'x' units/day and 'y' units/day, respectively. ATQ; 36 × (x + y) = 20 × (x + y) + 40y Or, 36x + 36y = 20x + 60y Or, 16x = 24y So, x = (3y/2) So, total work = 36 × {(3y/2) + y}  = 36 × (5y/2)  = '90y' units So, required time  = 90y ÷ y  = 90 days Alternate Solution Part of the work completed by 'X' and 'Y' together in 20 days = (20/36) = (5/9) Remaining part of the work = 1 - (5/9) = (4/9) which is completed by 'Y' alone in 40 days Therefore, time taken by 'Y' to complete the whole work alone  = 40 ÷ (4/9)  = 40 × (9/4)  = 90 days