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