**Percentage of a Number : **

In this section, we are going to learn, how to find percentage of a number.

**Percent of a number**** - Explanation**

To have better understanding on percent of a number, let us consider the following example.

**" 30 percent of 500 " **

30 percent means the value 30 is considered for one hundred.

If 30 is the value considered for 100, what value can be considered for 500 ?

It can be calculated as follows.

**30 % x 500 = 0.3 x 500 = 150**

The picture given below clearly illustrates "How to find percentage of a number"

Here, the "WH" question "what" has always to be replaced by some variable, say **"m"**

Sometimes, we will have the above question in a different method. It has been illustrated in the picture given below.

**Problem 1 :**

What is 20% of 50 ?

**Solution :**

Let us replace "what" by some variable, say "m"

m = 20% 50

m = 0.2 ⋅ 50

m = 10

Hence, 20% of 50 is 10.

**Problem 2 :**

If 20% of 30 is equal to m% of 60, find the value of "m".

**Solution :**

From the given information, we can have

20% of 30 = m% of 60

0.2 ⋅ 30 = (m/100) ⋅ 60

6 = 3m / 5

5/3 ⋅ 6 = m

10 = m

Hence, the value of "m" is 10.

**Problem 3 :**

If "m" percent of 500 is 75, what is m% of 700 ?

**Solution :**

Our first aim is to get the value of "m"

**Given :** "m" percent of 500 is 75

(m/100) ⋅ 500 = 75

5m = 75

m = 15

**Target :** m% of 700

m% of 700 = 15 % of 700

= 0.15 ⋅ 700

= 105

Hence, m% of 700 is 105.

**Problem 4 :**

David gets 20% income on $5000 investment per year. At the same rate, what is his income in 3 years ?

**Solution :**

**Income for one year : **

20% of 5000 = 0.2 ⋅ 5000 = 1000

**Income for 3 years :**

= 3 ⋅ 1000

= 3000

Hence, David's income for 3 years is $3000.

**Problem 5 :**

John gets 15% income on $2500 investment per year. At the same rate, what is his income for 2.5 years ?

**Solution :**

**Income for one year : **

15% of 2500 = 0.15 ⋅ 2500 = 375

**Income of 2.5 years :**

= 2.5 ⋅ 375

= 937.50

Hence, John's income for 2.5 years is $937.50

**Problem 6 :**

A gets 30% income on $7500 investment per year. If B gets the same income on $12500 investment per year, what is the percentage of income of "B" ?

**Solution :**

Let "m" be the percentage of income of B

From the given information, we have

30% of 7500 = m% of 12500

0.3 ⋅ 7500 = (m/100) ⋅ 12500

2250 = 125m

2250/125 = m

18 = m

Hence, the percentage of income of B is 18%.

**Problem 7 :**

A trader gets 25% profit on all the products. If the cost price of a particular product is $350, find his profit.

**Solution :**

Given : 25% profit on all the products

So, profit on $350 = 25% ⋅ 350

= 0.25 ⋅ 350

= 87.5

Hence, the required profit is $87.50

**Problem 8 :**

A trader gets $6.25 profit on a product whose cost price is $125.

What is profit percentage ?

**Solution :**

Let "m" be the required percentage.

From the given information, we can have

m% of 125 = 6.25

(m/100) ⋅ 125 = 6.25

m = (6.25/125) ⋅ 100

m = 5

Hence, the profit percentage is 5%.

After having gone through the stuff and examples, we hope that the students would have understood, "Percentage of a number"

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