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?
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 II
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