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    Question

    ‘A’ alone can complete a work in 65 hours. ‘A’ started the work alone and left after working on it for 40 hours. If ‘B’ completed the rest of the work in 25 hours then find the time taken by ‘A’ and ‘B’ together to complete the whole work.

    A 30.5 hours Correct Answer Incorrect Answer
    B 31.5 hours Correct Answer Incorrect Answer
    C 32.5 hours Correct Answer Incorrect Answer
    D 33.5 hours Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the total work = 260 units Then, efficiency of ‘A’ = (260/65) = 4 units/hour Work completed by ‘A’ alone in 40 hours = 4 × 40 = 160 units Remaining work = 260 – 160 = 100 units So, efficiency of ‘B’ = 100/25 = 4 units/hour Therefore, combined efficiency of ‘A’ and ‘B’ = 4 + 4 = 8 units/hour So, time taken by ‘A’ and ‘B’ together to complete the work = (260/8) = 32.5 hours

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