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?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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