Question
Quantity I. Two pipes A and B can fill a tank in 12
minutes and 16 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 9 minutes? Quantity II. Two pipes A and B can fill a tank in 24 minutes and 48 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 18 minutes? Study the following information carefully and answer the Questions given below:Solution
Quantity I. Let B be closed after x minutes. Then, part filled by (A + B) in x min. + part filled by A in (9 – x) min = 1 x (  1/12  +  1/16  ) +  (9 – x ) ×  1/12  = 1 Or  7x/48  +  (9-x)/12  = 1or  7 x + 36 – 4 x  = 48 ∴ 3 x = 12 or  x  = 4 Quantity II. 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  +  1/48  ) +  (18 – x ) ×  1/24  = 1 Or  3x/48  +  (18 -x)/24  = 1or  3 x + 36 – 2 x  = 48 ∴  x = 12 Hence Quantity I < Quantity IIÂ
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