Question
βXβ and βYβ together can finish an assignment in
30 days while βYβ and βZβ together can finish the same assignment in 45 days. βXβ and βYβ together worked on it for 20 days and then βZβ alone completed the remaining work in 15 days. If βXβ, βYβ, and βZβ started the assignment and worked together till its completion for which they received Rs. 1200 as total wage, then the share of βXβ out of the total wage will be:Solution
Let the total amount of work = 180 units (LCM of 30 and 45) Work done by βXβ and βYβ together in one day = 180 / 30 = 6 units Work done by βYβ and βZβ together in one day = 180 / 45 = 4 units Work done by βXβ and βYβ together in 20 days = 20 Γ 6 = 120 units Remaining work = 180 - 120 = 60 units Efficiency of βZβ = 60 / 15 = 4 units per day Efficiency of βYβ = 4 units (since Y and Z complete 4 units per day together) Efficiency of βXβ = 6 β 4 = 2 units per day Share of βXβ = (2 / (2 + 4 + 4)) Γ 1200 = 2/10 Γ 1200 = Rs 240
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