Question

Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. The tank is half fill. All 3 pipes are in operation simultaneously. After how much time will the tank be full?
A) $ 3\dfrac{9}{{17}} $ hours
B) 11 hours
C) $ 2\dfrac{8}{{11}} $ hours
D) $ 1\dfrac{{13}}{{17}} $ hours

Answer 1

Hint: The idea is simple, first we find the part filled in 1hr for individual pipes. Then we will have some parts that will get filled in 1hr. Then after that we will find the time to fill the full tank.

Complete step-by-step answer:
Here we are given that A can fill the tank in 5 hr
So, in 1hr it will fill $ \dfrac{1}{5} $ th of the tank.
Next, we will find the same for pipe B, so we are given that pipe B can fill the tank in 6hr so in 1hr it will fill $ \dfrac{1}{6} $ th of the tank
Again, we are given that pipe C can empty the tank in 12 hr
So, we will find the part of the tank it can empty in 1 hr
So, $ \dfrac{1}{{12}} $ th of the tank will get emptied in 1 hr.
 If three of the pipes are run at a time then A and B will fill the tank whereas C will remove the water from the tank.
Hence, we will add the part filled by A and B whereas we will subtract the part emptied by pipe C in 1 hr.
So, let’s do it, so if all the three pipes are run simultaneously, then the part filled in 1hr will be
 $ \dfrac{1}{6} + \dfrac{1}{5} - \dfrac{1}{{12}} $
So this will be: $ \dfrac{{10 + 12 + 5}}{{60}} = \dfrac{{27}}{{60}} $
This will be equal to 27 out of 60 part filled in 1 hr
So 1 full part gets filled in $ \dfrac{1}{{\left( {\dfrac{{17}}{{60}}} \right)}} $ hour
Hence $ \dfrac{{60}}{{17}} $ hr required to fill the total tank
Hence, we will convert this into mixed fraction so $ 3\dfrac{9}{{17}} $ hours.
So, the correct answer is “Option A”.

Note: While calculating the part that gets filled in 1 hr we will take care that the emptied part will be subtracted from the total value and the pipe that gets filled will be added. This is because our aim is to fill the tank and the things that go in favor of filling the tank will be added.