Question
βDβ and βEβ together can finish a task in 40
days, while βEβ and βFβ together can finish the same task in 30 days. βDβ and βEβ together worked on it for 35 days and then βFβ alone completed the remaining work in 10 days. If βDβ, βEβ, and βFβ started a certain task and worked together till its completion for which they received Rs. 1800 as total wage, then the share of βDβ out of the total wage will be:Solution
Let the total amount of work = LCM of 40 and 30 = 120 units Work done by βDβ and βEβ in one day = 120/40 = 3 units Work done by βEβ and βFβ in one day = 120/30 = 4 units Work done by βDβ and βEβ in 35 days = 35 Γ 3 = 105 units Remaining work = 120 - 105 = 15 units Efficiency of βFβ = 15/10 = 1.5 units per day Efficiency of βEβ = 4 - 1.5 = 2.5 units per day Efficiency of βDβ = 3 β 2.5 = 0.5 units per day Share of βDβ = (0.5 / (0.5 + 2.5 + 1.5)) Γ 1800 = Rs 200
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