Question
βXβ is 25% more efficient than βYβ, and βZβ
is 25% less efficient than βYβ. Together, they can complete a job in 40 days. If X and Y work together for 30 days, how long will Z take to finish the remaining work?Solution
Let efficiency of βYβ be βxβ units/day Efficiency of βXβ = 1.25x units/day Efficiency of βZβ = 0.75x units/day Total work = (1.25x + x + 0.75x) Γ 40 = 120x units Work done by X and Y in 30 days = 30 Γ (1.25x + x) = 67.5x units Remaining work = 120x β 67.5x = 52.5x units Time taken by Z = 52.5x Γ· 0.75x = 70 days
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