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 One pipe can fill a tank in (x2) hou...
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One pipe can fill a tank in (x2) hours and other pipe can empty the tank in (x+2) hours.If the tank is empty and both the pipes are opened together, the tank is filled in 24 hours.Find how much time will the second pipe take to empty the tank?
Expert Reply
Let us suppose the volume of the tank is V litres.
I pipe can fill the tank in x2 hrs.
So, volume filled in by I pipe in 1 hr, V_{in} = V/x2
II pipe can empty the tank in x+2 hrs.
So, volume emptied out by II pipe in 1hr, V_{out}= V/x+2
So, if the 2 pipes are turned on together
In 1 hour the total volume of the tank will be = V_{in}V_{out }= [V/x2 V/x+2]
In 24 hrs the total volume of the tank will be = 24[V/x2 V/x+2]
Since the tank is filled totally in 24 hrs so in 24 hr volume becomes equal to V
Hence 24[V/x2 V/x+2]=V
Or, x^{2}4 = 96
Or, x=10
Hence time taken by II pipe to empty the tank becomes x+2, =10+2 = 12 hrs.
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