Question

Kim fixed a red and a blue pipe in a tank. The red pipe takes 20 minutes and the blue pipe takes 25 minutes to fill the tank completely. Both the pipes are opened together, but at the end of 5 minutes, the blue pipe is turned off. How much longer will the tank take to fill?

• A. 10 minutes
• B. 13 minutes
• C. 11 minutes
• D. 12 minutes

Answer 1

The correct option is C 11 minutes

$\text{Let the volume of the tank}=\text{V}$

Let the rate at which the red pipe is filling $\text{the tank = R}$
And the rate at which the blue pipe is filling $\text{the tank = B}$

The red pipe fills the tank in 20 minutes.
The blue pipe fills the tank in 25 minutes.

$\text{So, R}=\frac{\text{V}}{20}$

$\text{And B}=\frac{\text{V}}{25}$

Let the time taken by the red pipe after the blue pipe is turned off to fill the $\text{tank}=t$

So,

$(\text{R}+\text{B})\times 5+\text{R}\times t=\text{V}$

$\Rightarrow (\frac{\text{V}}{20}+\frac{\text{V}}{25})\times 5+\frac{\text{V}}{20}\times t=\text{V}$

$\Rightarrow \frac{\text{V}}{4}+\frac{\text{V}}{5}+\frac{\text{V}t}{20}=\text{V}$

$\Rightarrow \frac{9\text{V}}{20}+\frac{\text{V}t}{20}=\text{V}$

$\Rightarrow \frac{\text{V}t}{20}=\text{V}–\frac{9\text{V}}{20}$

$\Rightarrow \frac{\text{V}t}{20}=\frac{(20–9)\text{V}}{20}$

$\Rightarrow \frac{\text{V}t}{20}=\frac{11\text{V}}{20}$

$\Rightarrow t=11$

So, the red pipe will take 11 more minute to fill the tank completely.