M05-23

Official Solution:

A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?

A. \(9\) liters
B. \(18\) liters
C. \(27\) liters
D. \(36\) liters
E. \(45\) liters


Let the rate of the draining pipe be \(x\) liters per hour. Then the capacity of the tank will be \(C=time*rate=4x\);

Now, when raining, the net outflow is \(x-3\) liters per hour, and we are told that at this new rate the pool is emptied in 6 hours. So, the capacity (C) of the pool also equals to \(C=time*rate=6(x-3)\);

Thus we have: \(4x=6(x-3)\). Solving gives \(x=9\). Therefore \(C=4x=36\).


Answer: D

Hi Bunuel , I have a doubt here. I had subtracted the rate of the drainage pipe from the rate of the rain (3-x) instead of (x-3) because the pool is being filled and the rain is pouring in the same direction whereas the draining pipe is doing the opposite action. Could you please clarify where am I going wrong with this concept? Thank you.

Please kindly explain the part "On a rainy day, the net outflow is x− 3 liters per hour" X-3 and not x + 3 liters per hour - just trying to understand that bit.