‘X’ and ‘Y’ together can finish an assignment in 30 days while ‘Y’ and ‘Z’ together can finish the same assignment in 45 days. ‘X’ and ‘Y’ together worked on it for 25 days and then ‘Z’ alone completed the remaining work in 15 days. If ‘X’, ‘Y’, and ‘Z’ started the assignment and worked together till its completion for which they received Rs. 1200 as total wage, then the share of ‘X’ out of the total wage will be: 

Solution

ATQ, Let the total amount of work = 180 units (LCM of 30 and 45)  Work done by ‘X’ and ‘Y’ together in one day = 90 / 30 = 3 units  Work done by ‘Y’ and ‘Z’ together in one day = 90 / 45 = 2 units  Work done by ‘X’ and ‘Y’ together in 25 days = 25 × 3 = 75 units  Remaining work = 90 - 75 = 15 units  Efficiency of ‘Z’ = 15 / 15 = 1 units per day  Efficiency of ‘Y’ = 1 units (since Y and Z complete 2 units per day together)  Efficiency of ‘X’ = 3 – 1 = 2 units per day  Share of ‘X’ = (2 / (1 + 1 + 2)) × 1200 = 2/4 × 1200 = Rs 600