Question
βPβ and βQβ together can complete an analysis in
40 days, while βQβ and βRβ together can complete the same analysis in 30 days. βPβ and βQβ together worked on it for 35 days and then βRβ alone completed the remaining work in 5 days. If βPβ, βQβ, and βRβ started the analysis and worked together till its completion for which they received Rs. 1200 as total wage, then the share of βPβ out of the total wage will be:ΒSolution
Let the total amount of work = 120 units (LCM of 40 and 30) Work done by βPβ and βQβ together in one day = 120 / 40 = 3 units Work done by βQβ and βRβ together in one day = 120 / 30 = 4 units Work done by βPβ and βQβ together in 35 days = 35 Γ 3 = 105 units Remaining work = 120 - 105 = 15 units Efficiency of βRβ = 15 / 5 = 3 units per day Efficiency of βQβ = 4 - 3 = 1 unit per day Efficiency of βPβ = 3 β 1 = 2 units per day Share of βPβ = (2 / (2 + 1 + 3)) Γ 1000 = 2/6 Γ 1200 = Rs 400
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