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    Question

    Two taps can fill a cistern in 20 hours and 13 hours,

    respectively. A third tap can empty it in 12 hours. How long will it take to fill the empty cistern, if all of them are opened together?  
    A 31(16/17) hours Correct Answer Incorrect Answer
    B 22(16/17) hours Correct Answer Incorrect Answer
    C 19(16/17) hours Correct Answer Incorrect Answer
    D 17(16/17) hours Correct Answer Incorrect Answer

    Solution

    Let’s assume the total work (i.e., filling the cistern) is 1 unit .

    • Tap A fills in 20 hours → Rate = 1/20
    • Tap B fills in 13 hours → Rate = 1/13
    • Tap C empties in 12 hours → Rate = −1/12 (since it removes water)
    Combine Rates Net rate when all three taps are open: (1/20) + (1/13) – (1/12) = 68/1560 Time to Fill the Cistern

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