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      Question

      Two pipes A and B can fill a tank in 12 min., and 16

      min, respectively. If both the pipes are opened simultaneously, after how much time A should be closed so that the tank is full in 12 minutes?
      A 3 min Correct Answer Incorrect Answer
      B 6 min Correct Answer Incorrect Answer
      C 5 min Correct Answer Incorrect Answer
      D 4 min Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let A be closed after x minutes. Then, Part filled by (A + B) in x min. + part filled by B in (12 – x) min. = 1  x (1/12   +  1/16   ) + (12 – x )  × 1/16   = 1  ⟹  (7 x)/48   +  (12 - x)/16    = 1 ⟹ (7 x)/48   +  3/4 - x/16   = 1 ⟹ (4 x)/48   = 1/4 ∴ x = 3  ∴ Hence, A must be closed after 3 minutes.

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