Problem 1 :
A pipe can fill up an empty tank in 12 minutes. Another pipe flows out 14 liter of water per minute. If the two pipes are opened together and the empty tank is filled up in 96 minutes, how much water does the tank contain ?
Let x liter of water filled in the tank per minute. So, y be the quantity of water in the tank
According to the given information, the empty tank is filled in 12 minutes by pumping x liter of water per minute.
y = 12x ---(1)
Now inlet and outlet both are opened and it is filled in 96 minutes.
y = 96x - 96(14) ------(2)
(1) = (2)
12x = 96x - 1344
84x = 1344
x = 16
By applying the value of x in (1), we get
y = 12 (16)
y = 192
So, the tank will contain 192 liter of water.
Problem 2 :
Two pipes are connected with a tank. The empty tank is filled up in t1 minutes by the first pipe and it becomes empty in t2 minutes by the second pipe. If the two pipes are opened together, how much time will the tank be filled up ? (Here t2 > t1)
Part of the tank filled by the first pipe in 1 hour = 1/t1
Part of the tank emptying by the second pipe in 1 hour = 1/t2
Part of the tank filled in 1 hour when both pipes are opened :
= 1/t1 - 1/t2
Time taken by both pipes to fill the tank
= t1t2 / (t2-t1)
Problem 3 :
A tank is filled up in 12 minutes by a pipe. Another pipe flows out 15 liter of water in 1 minute. When the tank is empty, the two pipes are opened together and the tank is filled up in 48 minutes. How much water does the tank contain ?
Let x liter of water filled in the tank in minute. So, y be the quantity of water in the tank.
According to the question
y = 12x ----(1)
When both pipes are opened and the tank is empty, if it filled in 48 minutes.
y = 48x - 15(48) ----(2)
(1) = (2)
12x = 48x - 720
12x-48x = -720
36x = 720
x = 720/36
x = 20
20 liter of water is pumped in the tank per minute.
By applying x = 20 in (1), we get
y = 12(20)
y = 240
So, 240 liter of water in the tank.
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