Question

If $x$ varies inversely as $y$, and $x=5$ when $y=2$ then for $y=5$, $x$ is

• A. $\frac{2}{5}$
• B. $2$
• C. $\frac{5}{2}$
• D. none of these

Answer 1

The correct option is B $2$

Given, $x$ varies inversely as $y$
$\Rightarrow x=k\cdot \frac{1}{y}$ where $k$ is a constant
Now given that, at $x=5,y=2$ putting this in above equation
$\Rightarrow 5=k\left(1/2\right)\Rightarrow k=10$
Thus our equation becomes $x=\frac{k}{y}=\frac{10}{y}$
Hence at $y=5,x=\frac{10}{5}=2$