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    Question

    Tap ‘A’ and tap ‘B’ can fill a tank in 64 hours

    and 56 hours, respectively. If both taps are opened together, then find the time after which tap ‘A’ must be closed so the whole tank can be filled in 21 hours.
    A 16 hours Correct Answer Incorrect Answer
    B 20 hours Correct Answer Incorrect Answer
    C 24 hours Correct Answer Incorrect Answer
    D 40 hours Correct Answer Incorrect Answer

    Solution

    Let total capacity of the tank is 448 litres (LCM of 64 and 56) Quantity of water filled by tap ‘A’ in one hour = 448/64 = 7 litres Quantity of water filled by tap ‘B’ in one hour = 448/56 = 8 litres Let tap ‘A’ is closed after ‘x’ hours So, 15 × x + 8 × (21 – x) = 448 Or, 7x = 280 Or, x = 40 hours

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