Question
‘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 20 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
Let the total amount of work = 180 units (LCM of 30 and 45) Work done by ‘X’ and ‘Y’ together in one day = 180 / 30 = 6 units Work done by ‘Y’ and ‘Z’ together in one day = 180 / 45 = 4 units Work done by ‘X’ and ‘Y’ together in 20 days = 20 × 6 = 120 units Remaining work = 180 - 120 = 60 units Efficiency of ‘Z’ = 60 / 15 = 4 units per day Efficiency of ‘Y’ = 4 units (since Y and Z complete 4 units per day together) Efficiency of ‘X’ = 6 – 4 = 2 units per day Share of ‘X’ = (2 / (2 + 4 + 4)) × 1200 = 2/10 × 1200 = Rs 240
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