The result of any division in which the divisor is 100 is a percentage. The divisor, i.e., 100 is denoted by a special symbol %. .

For example, = 10%

= 25%

= x%

Since any ratio is also basically a division, each ratio can also be expressed as a percentage. The terms “ratio” and “percentage” can be used interchangeably along with the corresponding mention of the denominator being taken as 100. 1 .

For example a ratio of can be converted to a percentage figure as = 50 percentage

“Percentage” is also referred to as “percent”. .

The term percent means one out of every hundred. By a certain percent we mean that many hundredths. For example, 15 percent means 15 out of hundred (or) 15 hundredths. The symbol % is used to denote percent. .

x% = x out of 100 =

So, 75% = 75 out of 100 =

Any percentage can be expressed as a decimal fraction by dividing the percentage figure by 100. .

Any decimal fraction can be converted into percentage by multiplying it by 100. .

0.5 = = 50%

0.25 = = 25%

0.2 = = 20%

**Note: **

(1) When two numbers x and y are given, then one number can be expressed as a percentage of the other, in the following way. .

x as a percent of y = x 100

y as a percent of x = x 100

(2) x% of y = y% of x

If a number is increased by 45%, then it becomes 116. What is the number? .

Let the number be x. According to the problem. .

x + 45% of x = 116. .

&⇒ x + x = 116

&⇒ x =

&⇒ x = 80. .

\ The required number is 80. .

36% of the maximum marks in an examination is equal to 756 marks. What is 54% of the maximum marks in it? .

Let the total be x. .

36% of x = 756

x x = 756

x = 756 x = 21 x 100

x = 2100

54% of 2100 is x 2100 = 1134

There are three terms. The second and third terms are 20% and 80% more than the first. What percentage of the second term is the third? .

Let the first term be 100. Then the second and third terms will become 120 and 180. .

Let the third term be x% of the second. .

x% of 120 = 180

x 120 = 180

x = x 100

x = 150

Two candidates contested in an election. The candidate favoured by 38% of the votes is rejected by a majority of 18924 votes. Find the total number of valid votes. .

Let the total number of votes polled be x. .

Majority = 18924

i.e., 62% of x - 38% of x = 18924 .

&⇒ 24% of x = 18924

&⇒ x x = 18924

&⇒ x =

&⇒ x = 78850

\ The total number of valid votes polled were 78850. .

Anil spends 40% of his income on rent, 30% of the remaining on medicines, 20% of the remaining on education. If he saves Rs.840 every month, find his monthly salary. .

Let’s Anil’s salary be Rs.100. .

Money spent on rent = 40% of 100 = Rs.40. .

Money spent on medicines = 30% of (100 - 40)

= x 60 = Rs.18

Money spent on education = 20% of (60 - 18)

= x 42

= Rs.8.40 .

Anil saves 100 - (40 + 18 + 8.40) i.e. Rs.33.60 .

When savings are Rs.33.6, salary is Rs.100. .

When savings are Rs.840, total salary .

= x 100.

i.e Rs.2500. .