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?Solution
Quantity I. Let B be closed after x minutes. Let total capacity of tank = LCM (12 & 16) = 48 L So A’ 1 min work = 48/12 = 4L B’s 1 min work = 48/16 = 3L So as per the question, 4×9 +3×x= 48 or 3x = 12 or x =4min Quantity II. Let B be closed after minutes. Let total capacity of tank = LCM (24 & 48) = 48 L So A’ 1 min work = 48/24 = 2L B’s 1 min work = 48/48 = 1L So as per the question, 18×2 +1×x= 48 or x = 12 Hence Quantity I < Quantity II
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