Question

y varies inversely with x. If y = 30 when x = 12, find
(1) y when x = 15
(2) x when y = 18

Answer 1

Since, y varies inversely with x.

$$\begin{gathered} \Rightarrow y\propto \frac{1}{x} \\ \Rightarrow y=\frac{k}{x},\mathrm{where}k\mathrm{is}\mathrm{proportioanlity}\mathrm{constant}. \end{gathered}$$

We have, y = 30 and x = 12,

$$\begin{gathered} \Rightarrow 30=\frac{k}{12} \\ \Rightarrow k=30\times 12 \\ \Rightarrow k=360 \\ \mathrm{So},y=\frac{360}{x}...\left(\mathrm{i}\right) \end{gathered}$$

(1) We have, x = 15

By using equation (i), we get

$y=\frac{360}{15}=24$

(2) We have, y = 18

By using equation (i), we get

$$\begin{gathered} 18=\frac{360}{x} \\ \Rightarrow x=\frac{360}{18}=20 \end{gathered}$$