### Theory:

1. Finding a percentage of a given number:

To find the percentage of a given number, multiply the number by the require percent.

Let the number $$= x$$

Require percent $$= p$$$$\%$$

Percentage of given number $$= p$$$$\%$$ of $$x$$

$$=$$ $\frac{p}{100}×x$

2. Finding the original number from its percent:

Let original number $$= x$$

Require percent $$= p$$$$\%$$

Obtained percentage $$= y$$

Now $$p$$$$\%$$ of $$x = y$$

$\frac{p}{100}×x$ $$= y$$

$$x =$$ $\frac{y}{p}×100$

Number $$=$$ $$\frac{\text{Obtained percentage}}{\text{percent}}$$$$\times100$$

3. Finding how much percent one quantity is of another quantity:

To find what percent of one quantity is of the other quantity if two quantities are given, we proceed as:

Let $$a$$ and $$b$$ are two quantities and we want to know 'what percent of $$a$$ is $$b?$$'.

Let $$x$$$$\%$$ of $$a$$ is equal to $$b$$ then:

$\begin{array}{l}\frac{x}{100}×a=b\\ \\ x=\frac{b}{a}×100\end{array}$