Question
βPβ, βQβ and βRβ can finish a task in 12
days, 36 days and 72 days respectively. βPβ and βQβ begin the task. After βnβ days, βPβ leaves and βRβ joins βQβ. If the total work is completed in 20 days, find the value of 2n.Solution
ATQ,
Let the total work be 72 units (LCM of 12, 36, 72) Efficiency of βPβ = 72 / 12 = 6 units/day Efficiency of βQβ = 72 / 36 = 2 units/day Efficiency of βRβ = 72 / 72 = 1 unit/day ATQ, (6 + 2) Γ n + (2 + 1) Γ (20 - n) = 72 Or, 8n + 3(20 - n) = 72 Or, 8n + 60 - 3n = 72 Or, 5n = 12 Or, n = 2.4 Required value = 2 Γ 2.4 = 4.8
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