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    Question

    β€˜X’ can finish 50% of a job in 8 days. β€˜Y’ takes

    8 days more than β€˜X’ to complete the entire work, and Y is 20% more efficient than β€˜Z’. β€˜X’ starts the task alone, on 2nd day he is joined by β€˜Y’ only, on 3rd day, he is joined by β€˜Z’ only, and on 4th day, he again works alone. They follow this same pattern for 9 days. The combined time taken by β€˜X’ and β€˜Y’ alone to finish the leftover work is how much percent more/less than that by β€˜Z’ alone?
    A 10% less Correct Answer Incorrect Answer
    B 15% more Correct Answer Incorrect Answer
    C 25% less Correct Answer Incorrect Answer
    D 32% more Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    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 – 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 – 16.8) / 16.8) Γ— 100 = 15% more

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