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    Question

    β€˜A’ alone can complete a work in 50 hours. β€˜A’

    started the work alone and left after working on it for 40 hours. If β€˜B’ completed the rest of the work in 10 hours then find the time taken by β€˜A’ and β€˜B’ together to complete the whole work.
    A 21 hours Correct Answer Incorrect Answer
    B 22 hours Correct Answer Incorrect Answer
    C 25 hours Correct Answer Incorrect Answer
    D 23 hours Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the total work = 200 units Then, efficiency of β€˜A’ = (200/50) = 4 units/hour Work completed by β€˜A’ alone in 40 hours = 4 Γ— 40 = 160 units Remaining work = 200 – 160 = 40 units So, efficiency of β€˜B’ = 40/10 = 4 units/hour Therefore, combined efficiency of β€˜A’ and β€˜B’ = 4 + 4 = 8 units/hour So, time taken by β€˜A’ and β€˜B’ together to complete the work = (200/8) = 25 hours

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