- There are 12 pipes attached to a tank. Some of them are fill pipes and
some are drain pipes. Each of the fill pipes can fill the tank in 12 hours,
while each of the drain pipes will take 24 hours to drain a full tank
completely. If all the pipes are kept open when the tank was empty, it takes
2 hours for the tank to overflow. How many of these pipes are drain pipes?
(1) 6 (2) 11 (3) 4 (4) 7
Solution:
There are 12 pipes attached to the tank. Let �n� of them be fill pipes.
Therefore, there will be 12-n drain pipes.
Each fill pipe, fills the tank in 12 hours. Therefore,
1/12th
of the tank gets filled every hour by one fill pipe.
�n� fill pipes will, therefore, fill
n/12 th
of the tank in an hour.
Each drain pipe drains the tank in 24 hours. That is,
1/24 th
of the tank gets drained by one drain pipe every hour.
12-n drain pipes, will therefore, drain
12-n / 24 th
of the tank in an hour.
When all the pipes are open when the tank is empty, it takes 2 hours for the
tank to overflow. i.e. � the tank gets filled every hour.
Equating the information, we get
n/12 - 12-n/24 = 1/2
=> 2n+n-12 / 24 = 1/2
=> 3n - 12 = 12 or 3n = 24 or n = 8.
Therefore, there are 8 fill pipes and (12 - 8) = 4 drain pipes.
