Question
βAβ is 25% less efficient than βBβ, and βCβ
is 75% more efficient than βBβ. All three together complete a task in 32 days. After βAβ and βBβ work together for 16 days, they stop. How long will βCβ take to finish the remaining work?Solution
Let efficiency of βBβ = x units/day
Efficiency of βAβ = 0.75x units/day
Efficiency of βCβ = 1.75x units/day Total work = (x + 0.75x + 1.75x) Γ 32 = 3.5x Γ 32 = 112x units Work done by βAβ and βBβ in 16 days = (x + 0.75x) Γ 16 = 1.75x Γ 16 = 28x units Remaining work = 112x β 28x = 84x units Time required by βCβ = 84x / 1.75x = 48 days
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