The following problems on percentages will explain how to perform various operations on percentages, like adding, subtracting, multiplying and dividing.

**Example 1**

There are 100 students in a class, out of which 60 are girls. Express the number of boys and girls as percentage.

**Solution:**

Number of girls = 60

There are 60 girls out of a total of 100 students, which we can represent as $\frac{60}{100}$ .

Hence 60% of the students are girls.

Number of boys = 100 -60 =40

So, 40 out of 100 students are boys.

In other words 40% of the students are boys.

**Example 2**

There are 50 balls in a bag out of which 28 are red, 15 are blue and the rest are green. Represent the number of balls of each color as a percentage.

**Solution:**

28 out of 50 balls are red. As a fraction we can represent this as $\frac{28}{50}$

$\frac{28}{50}$ = $\frac{28}{50}$ x $\frac{100}{100}$

= $\frac{(28\times100)}{(50\div100)}$

= $\frac{(28\times100)}{50}$ %

= 56%

There are 15 blue balls in the bag. As a fraction, we can say $\frac{15}{50}$ are blue

$\frac{15}{50}$ = $\frac{15}{50}$ × $\frac{100}{100}$

= $\frac{(15\times100)}{(50\div100)}$

= $\frac{30}{100}$

= 30%

The number of green balls is 7. So we have $\frac{7}{50}$ are green

$\frac{7}{50}$ = $\frac{7}{50}$ × $\frac{100}{100}$

= $\frac{(7\times1000)}{(50\div100)}$

= $\frac{14}{100}$

= 14%

In other words we know 56% of balls are red, 30% of balls are blue and so the remaining 14%( 100-(56+3)) will be green.

**Example 3**

What percentage of 200 is 24

**Solution:**

Let us assume that x % of 200 is 24

So we write $\frac{x}{100}$ 200 = 24

X x 2= 24

x = 12

Hence 12 % of 200 is 24

**Example: 4**

Write the given ratios as a fraction and percents.

(a) 4: 100 (b) 12: 25 (c) 17: 100 (d) 63: 75

**Solution:**

(a) Given, ratio = 4: 100

Therefore, Fraction = $\frac{4}{(100)}$

Percent = $\frac{4}{(100)}$ × 100 = 4%

(b) Given, ratio = 12: 25

Therefore, Fraction = $\frac{(12)}{(25)}$

Percent = $\frac{(12)}{(25)}$ × 100 = 48%

(c) Given, ratio = 17: 100

Therefore, Fraction = $\frac{(17)}{(100)}$

Percent = $\frac{(17)}{(100)}$ × 100 = 17%

(d) Given, ratio = 63: 75

Therefore, Fraction = $\frac{(63)}{(75)}$

Percent = $\frac{(63)}{(75)}$ × 100 = 84%

**Example: 5**

Write each percent as a ratio

(a) 25% (b) 30% (c) 52% (d) 100%

**Solution:**

(a) Given, Percent = 25%

Therefore, fraction = $\frac{(25)}{(100)}$ = $\frac{1}{4}$

Ratio = 1: 4

(b) Given, Percent = 30%

Therefore, fraction = $\frac{(30)}{(100)}$ = $\frac{3}{(10)}$

Ratio = 3: 10

(c) Given, Percent = 52%

Therefore, fraction = $\frac{(52)}{(100)}$ = $\frac{(13)}{(25)}$

Ratio = 13: 25

(d) Given, Percent = 100%

Therefore, fraction = $\frac{(100)}{(100)}$ = $\frac{1}{1}$

Ratio = 1: 1