- A pump can be used either to fill or to empty a tank. The capacity of
the tank is 3600 m3. The emptying capacity of the pump is 10 m3/min
higher than its filling capacity. What is the emptying capacity of the pump
if the pump needs 12 more minutes to fill the tank than to empty it?
(1) 50 m3 / min (2) 60 m3 / min (3) 45 m3 / min (4) 90 m3 /min
Solution:
Let �f� m3/min be the filling capacity of the pump. Therefore, the emptying capacity of the pump will be = (f + 10 ) m3 / min.
The time taken to fill the tank will be = 3600 / f minutes
And the time taken to empty the tank will be = 3600 / f+10.
We know that it takes 12 more minutes to fill the tank than to empty it
i.e 3600/f - 3600 / f+10 = 12
=> 3600 f + 36000 - 3600 f = 12 (f2 + 10 f)
=> 36000 = 12 (f2 + 10 f) => 3000 = f2 + 10 f => f2
+ 10 f - 3000 = 0.
Solving for positive value of �f� we get, f = 50.
Therefore, the emptying capacity of the pump = 50 + 10 = 60 m3 / min
