Question

24 pipes, all of them of the same size can fill a tank in 112 mins. If 10 pipes are closed, then how much time will it take to fill the tank?

• A. $190mins$
• B. $192mins$
• C. $182mins$
• D. $200mins$

Answer 1

The correct option is B $192mins$

Given, 24 pipes can fill a tank in 112 mins.

We know that, lesser the number of pipes, more will be the time taken to fill the tank.

$\text{So, Number of pipes}\left(x\right)\propto \frac{1}{\text{Time}\left(y\right)}$
$\therefore \frac{x_1}{x_2}=\frac{y_2}{y_1}$

Given,
$x_1=24pipes$
$y_1=112mins$
$x_2=24-10=14pipes$
$\text{and}{y}_2=\text{time taken by 14 pipes}$

$\Rightarrow \frac{24}{14}=\frac{y_2}{112}$
$\Rightarrow 24\times 112=14\times y_2$
$\Rightarrow y_2=\frac{24\times 112}{14}=192mins$

So, it will take 192 minutes to fill the tank with 10 pipes closed.