# Overview

## Basic Concept

Percentage - a number expressed as a fraction of 100, i.e. per 100. (Percent means “Per 100”) It is the numerator of the ratio whose denominator (or base) is 100. It is represented by “%”

1 per 4

To convert any ratio into percentage we need to make the denominator 100.Out of 4 – work completed 1

Out of 1 – work completed $( \frac{1}{4} $)

Out of 100 – work completed $( \frac{1}{4} $) × 100 = 25%

More Examples:

$( \frac{50}{200} $) = $( \frac{25}{100} $) = 25%

$( \frac{40}{50} $) = $( \frac{80}{100} $) = 80%

To convert a percentage into fraction, divide it by 100.

25% ≡ 0.25 - that is a ratio of 1:4

(% ≡ $( \frac{1}{100} $))

Percent Formula:

x as a percentage of y = $( \frac{x}{y} $) × 100%

x as a percentage of y = $( \frac{x}{y} $) × 100%

###### Q. What percent of 60 is 15?

Explanation :

x as a percentage of y = $( \frac{x}{y} $) × 100%

15 as a percentage of 60 = $( \frac{15}{60} $) × 100% = $( \frac{1}{4} $) × 100% = 25%

x as a percentage of y = $( \frac{x}{y} $) × 100%

15 as a percentage of 60 = $( \frac{15}{60} $) × 100% = $( \frac{1}{4} $) × 100% = 25%

###### Q. Find the number whose 40% is 120.

Explanations :

Explanation 1:

x as a percentage of y = $( \frac{x}{y} $) × 100% (Here y is not known.)

40 % = $( \frac{120}{y} $) × 100%

Or y = $( \frac{120}{40} $) × 100% = 300

x as a percentage of y = $( \frac{x}{y} $) × 100% (Here y is not known.)

40 % = $( \frac{120}{y} $) × 100%

Or y = $( \frac{120}{40} $) × 100% = 300

Explanation 2:

Let the unknown number be y

40 % of y = 120

Or $( \frac{40}{100} $) × y = 120

Or y = 300

Let the unknown number be y

40 % of y = 120

Or $( \frac{40}{100} $) × y = 120

Or y = 300

Explanation 3:

40 % of the unknown number = 120

80 % of the unknown number = 240

100 % of the unknown number = 300

40 % of the unknown number = 120

80 % of the unknown number = 240

100 % of the unknown number = 300

###### Q. x% of x = 64. Find x

Explanation :

x % of x = 64

Or $( \frac{x}{100} $) × x = 64

Or $x^2 $ = 6400

Or x = 80

Or $( \frac{x}{100} $) × x = 64

Or $x^2 $ = 6400

Or x = 80

## Tip

x% of y = x/100 × y % = xy/100 %

y% of x = y/100 × x % = xy/100 %

x% of y = y% of x

###### Q. Find 8% of 50.

Explanation :

8% of 50 is the same as 50% of 8

And 50% of 8 is 4

So 8% of 50 must also be 4

And 50% of 8 is 4

So 8% of 50 must also be 4