Question

If $x$ varies directly as $y$ and $x=12$ when $y$ is $48$ then$x=6$ when $y$ is?

Answer 1

If $x$ varies directly as $y$ then

$\frac{x}{y}=k$

When, $x=12$ and $y=48$

$k=\frac{12}{48}=\frac{1}{4}$

Now, $x=6$ and $k=\frac{1}{4}$, then;

$$\begin{gathered} \Rightarrow \frac{x}{y}=k \\ \Rightarrow y=\frac{x}{k} \\ \Rightarrow y=6\times 4=24 \end{gathered}$$

Hence $y$ is $24$.