If x % of x is 25, then the value of x is:

The correct answer is Option (2) → 50

\(x\%\) of a quantity means \(\frac{x}{100}\) times that quantity, so \(x\%\) of \(x\) is \(\frac{x}{100}\times x=\frac{x^{2}}{100}\). Here the same \(x\) is both the percentage and the quantity it is taken of, so it appears twice and the equation has \(x^{2}\) in it.

• \(x\%\) of \(x\) is 25: \(\displaystyle\frac{x^{2}}{100}=25\), so \(x^{2}=2500\)

• The positive square root: \(x=50\), since \(50\times50=2500\)