# 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%
###### 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%
###### 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
Explanation 2:
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
###### 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

## 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
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