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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?ย ย 
      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

      Letโ€™s assume the total work (i.e., filling the cistern) is 1 unit .

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

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