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    Question

    Aman, Rahul and Pratik working together completed a job

    in 10 days. The ratio of their efficiencies is 5: 4 : 3. How many days will be required by the fastest worker alone to complete the whole work?
    A 24 days Correct Answer Incorrect Answer
    B 48 days Correct Answer Incorrect Answer
    C 27 days Correct Answer Incorrect Answer
    D 20 days Correct Answer Incorrect Answer

    Solution

    Ratio of efficiencies = 5 : 4 : 3 Ratio of time required = 1/5 : 1/4 : 1/3 = 12 : 15 : 20 Suppose Aman, Rahul and Pratik complete the work in 12x, 15x, 20x days respectively. Then, 1/(12 x) + 1/( 15 x) + 1/( 20 x) = 1/10 (5x+4x+3x)/60x = 1/10 12/60x = 1/10 x = (12×10)/60 = 2 days Hence, the fastest worker Aman can complete the work = 12x = 12 × 2 = 24 days

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