Question

Two pipes A and B can fill a water tank in 20 minutes and 24 minutes, respectively, and the third pipe C can empty at the rate of 3 gallons per minute. If A, B and C opened together, fill the tank in 15 minutes the capacity (in gallons) of the tank is
$$\begin{gathered} \left(a\right)180 \\ \left(b\right)150 \\ \left(c\right)120 \\ \left(d\right)60 \end{gathered}$$

Answer 1

Hint: If a pipe fills the tank in x minute so we can write as water supplied by pipe is equal ${\displaystyle \frac{V}{x}}$, where V is the volume of the tank. So, for the solution we use this concept.

Complete step-by-step answer:

Let the volume (capacity) of tank be V gallons
Time taken by A pipe to fill a water tank =20 minutes
Water supplied by Pipe A $={\displaystyle \frac{V}{20}}$
Time taken by B pipe to fill a water tank =24 minutes
Water supplied by Pipe B $={\displaystyle \frac{V}{24}}$
Time taken to the fill tank when all A, B and C pipes opened together =15 minutes
Water supplied when all A, B and C pipes are working $={\displaystyle \frac{V}{15}}$
The third pipe C can empty at the rate of 3 gallons per minute.
So, ${\displaystyle \frac{V}{20}}+{\displaystyle \frac{V}{24}}-3={\displaystyle \frac{V}{15}}$
$\Rightarrow {\displaystyle \frac{V}{20}}+{\displaystyle \frac{V}{24}}-{\displaystyle \frac{V}{15}}=3$
Take LCM of 20, 24 and 15.
$$\begin{gathered} \Rightarrow {\displaystyle \frac{6V+5V-8V}{120}}=3 \\ \Rightarrow 11V-8V=360 \\ \Rightarrow 3V=360 \\ \Rightarrow V=120 \end{gathered}$$
The capacity of the tank is 120 gallons.
So, the correct option is (c).

Note: Whenever we face such types of problems we use some important points. First we find the water supplied by single pipes to the tank and also find the water supplied by all pipes to the tank then water supplied by all pipes is equal to difference of water supplied by single pipes and water empty by pipe.