Arithmetic

Percentages

Hard

If $x\%$ of $y$ is equal to $z$ then what percentage of $z$ is $x$ ?

$\frac{y^2}{100}$

$\frac{x^2}{100}$

$\frac{100^2}{y}$

$\frac{100^2}{x}$

✅ Correct Option: 3

$x\%$ of $y=\frac{xy}{100}=z$ --> Eq. 1

We are to find what percentage of $z$ is $x$ , hence we are to find $\frac{100x}{z}$

Let's go back to Eq. 1 and manipulate it a bit.

First, let's divide both sides by $y$ :

$\frac{x}{100}=\frac{z}{y}$

Now let's multiply both sides by $100\times100$

$100x=\frac{100^2z}{y}$

Now divide both sides by $z$

$\frac{100x}{z}=\frac{100^2}{y}$

Hence, Option 3 is correct.

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