Question

If $\frac{1}{5}:\frac{1}{\mathrm{x}}=\frac{1}{\mathrm{x}}:\frac{1}{125}$ then the value of $\mathrm{x}$ is

• A. $15$
• B. $20$
• C. $25$
• D. $35$

Answer 1

The correct option is C

$25$

Explanation for the correct answer:

$\frac{1}{5}:\frac{1}{\mathrm{x}}=\frac{1}{\mathrm{x}}:\frac{1}{125}$

$\Rightarrow$ $\frac{1}{5}\times \frac{1}{125}=\frac{1}{\mathrm{x}}\times \frac{1}{\mathrm{x}}$ $...(\mathrm{a}:\mathrm{b}=\mathrm{c}:\mathrm{d}\Rightarrow \mathrm{ad}=\mathrm{bc})$

$\Rightarrow$ $\frac{1}{625}=\frac{1}{{\mathrm{x}}^2}$

$\Rightarrow$ ${\mathrm{x}}^2=625$

$\Rightarrow$ $\mathrm{x}=25$

Hence, the value of $\mathrm{x}$ will be $25$, so, option$\left(\mathrm{C}\right)$ is the correct answer.