Question

$12$ pipes, all of the same size, fill a tank in $42$ minutes. How long will it take to fill the same tank, if $21$ pipes of the same size are used?

Answer 1

Step 1: Framing the table for given information

Let the time taken to fill the same tank with $21$ pipes be $x$ minutes.

Framing the table for given information:

$\begin{array}{ccc}\text{Number of pipes}& 12& 21\\ \text{Time (in minutes)}& 42& x\end{array}$

Let $x_1=12,x_2=21$

$y_1=42,y_2=x$

Step 2: Solve using inverse relation

Here, the number of pipes and time taken to fill the tank are varying inversely.

So, $x_1{y}_1=x_2{y}_2$

$\Rightarrow 12\times 42=21\times x$

$\Rightarrow x=\frac{12\times 42}{21}=24\text{minutes}$

Therefore, the time taken to fill the same tank with $21$ pipes is $24$ minutes.