Question
βXβ can finish 50% of a job in 8 days. βYβ takes
8 days more than βXβ to complete the entire work, and Y is 20% more efficient than βZβ. βXβ starts the task alone, on 2nd day he is joined by βYβ only, on 3rd day, he is joined by βZβ only, and on 4th day, he again works alone. They follow this same pattern for 9 days. The combined time taken by βXβ and βYβ alone to finish the leftover work is how much percent more/less than that by βZβ alone?Solution
ATQ,
Time taken by X to complete the work = 8 / 0.5 = 16 days Time taken by Y = 16 + 8 = 24 days Time taken by Z = 24 Γ 1.20 = 28.8 days Let total work = 576 units Efficiency of X = 576 / 16 = 36 units/day Efficiency of Y = 576 / 24 = 24 units/day Efficiency of Z = 576 / 28.8 = 20 units/day Work done in 3 days = 36 + 24 + 20 = 80 units Work done in 9 days = 80 Γ 3 = 240 units Remaining work = 576 β 240 = 336 units Time by X = 336 / 36 = 9.33 days Time by Y = 336 / 24 = 14 days Time by Z = 336 / 20 = 16.8 days Required % = ((9.33 + 14 β 16.8) / 16.8) Γ 100 = 15% more
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