Question
Two pipes A and B can fill a tank in 24 min., and 32
min, respectively. If both the pipes are opened simultaneously, after how much time B should be closed so that the tank is full in 18 minutes?Solution
Let B be closed after x minutes. Then, Part filled by (A+B) in x min. + part filled by A in (18 – x) min. = 1 x (1/24 + 1/32 ) + ( 18 – x ) × 1/24 = 1 ⟹ 7x/96 + (18-x)/24 = 1 ⟹7 x + 4 (18 – x) = 96 ∴ x = 8 ∴ Hence, B must be closed after 8 minutes
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