In this chapter, we will try to calculate the percentage value of one number to another.

In other words, we will try to find how much percentage does one number is of another.

We have also provided some problems at the end of the chapter for your practice.

## Representing two numbers in form of percentage.

Let two numbers are given** 2 and 50**.

How much percentage does 2 represents as that of number 50.

To find the percentage value, **use the following formula**;

\mathtt{Percentage\ =\frac{Given\ number\ }{Reference\ number} \times 100}

**In the above example;**

Given number = 2

Reference number = 50

Putting the values in formula;

\mathtt{Percentage=\ \frac{2}{50} \times 100}\\\ \\ \mathtt{Percentage\ =\ \frac{\cancel{2}}{\cancel{50} \ 25} \times 100}\\\ \\ \mathtt{Percentage\ =\ 4\%}

Hence, **number 2 is 4% of number 50**.**Note:**

Both the numerator and denominator should be in same format.

If the numerator value is given in kilogram, then denominator value should also be in kilogram.

I hope you understood the above concept. Let us see some solved examples for better understanding.

**Example 01**

Calculate the percentage value of number 30 of 360.

**Solution**

\mathtt{Percentage=\ \frac{30}{360} \times 100}\\\ \\ \mathtt{Percentage\ =\ \frac{\cancel{30}}{\cancel{360} \ 12} \times 100}\\\ \\ \mathtt{Percentage\ =\ 8.33\%}

Hence, **number 30 is 8.33% of number 360**.

**Example 02**

Shane scored 50 marks out of 120. Calculate the percentage.

**Solution**

\mathtt{Percentage\ =\frac{marks\ scored\ }{total\ marks} \times 100}\\\ \\ \mathtt{Percentage=\ \frac{50}{120} \times 100}\\\ \\ \mathtt{Percentage\ =\ 41.67\%}

Hence, **Shane scored 41.67% of the marks.**

**Example 03**

Express 30kg as percentage of 900 kg.**Solution**

\mathtt{Percentage\ =\frac{given\ weight\ }{total\ weight} \times 100}\\\ \\ \mathtt{Percentage=\ \frac{30}{900} \times 100}\\\ \\ \mathtt{Percentage\ =\ 3.33\%}

Hence, **3.33% is the solution.**

**Example 04**

Anthony has 12 Million dollars in Bank A. The total wealth of Anthony is 60 Million dollars. How much percentage of wealth is kept in Bank A.

**Solution**

\mathtt{Percentage\ =\frac{money\ in\ Bank\ A\ }{total\ wealth} \times 100}\\\ \\ \mathtt{Percentage=\ \frac{12}{60} \times 100}\\\ \\ \mathtt{Percentage\ =\ 20\%}

Hence, **20% of Anthony wealth is kept in Bank A.**

**Example 05**

Express 120 ml as percentage of 9 liters.**Solution**

Note that both the given numbers are in different format.

To calculate the percentage, express the number in same format.

we know that;

1 liter = 1000 ml**Given number = 120 ml****Reference number **= 9 x 1000 ml = **9000 ml**

Now calculating the percentage;

\mathtt{Percentage\ =\frac{given\ number\ }{reference\ number} \times 100}\\\ \\ \mathtt{Percentage=\ \frac{120}{9000} \times 100}\\\ \\ \mathtt{Percentage\ =\ 1.33\%}

Hence, **120ml is 1.33% of 9 liter**.

I hope you understood the above examples. Given below are solved problems for further practice.

## Calculating percentage value – Solved examples

**(01) Find the percentage value of given numbers.**

(a) Express 2.5 as percent of 300

(b) Express 0.1 as percent of 40

(c) 600 as percent of 9600

(d) 25 as percent of 1500

(e) 3 as percent of 10

Solution

**(a) Express 2.5 as percentage of 300**

\mathtt{Percentage=\ \frac{2.5}{300} \times 100}\\\ \\ \mathtt{Percentage\ =\ 0.83\%} **Hence, 0.83% is the solution.**

**(b) Express 0.1 as percentage of 40**

\mathtt{Percentage=\ \frac{0.1}{40} \times 100}\\\ \\ \mathtt{Percentage\ =\ 0.25\%}

Hence, **0.25% is the solution.**

**(c) 600 as percentage of 9600**

\mathtt{Percentage=\ \frac{600}{9600} \times 100}\\\ \\ \mathtt{Percentage\ =\ 6.25\%}

Hence, **6.25% is the solution.**

**(d) 25 as percentage of 1500**

\mathtt{Percentage=\ \frac{25}{1500} \times 100}\\\ \\ \mathtt{Percentage\ =\ 1.67\%}

Hence, **1.67% is the solution**.

**(e) 3 as percentage of 10 **

\mathtt{Percentage=\ \frac{3}{10} \times 100}\\\ \\ \mathtt{Percentage\ =\ 30\%}

Hence, **30% is the solution.**

**(02)** In grade 8 examination, the total marks scored by Rachel in all subject is 420 out of 500. Express the result of Rachel in form of percentage.

**Solution**

Marks scored = 420

Total marks = 500

\mathtt{Percentage\ =\frac{marks\ scored\ }{total\ marks} \times 100}\\\ \\ \mathtt{Percentage=\ \frac{420}{500} \times 100}\\\ \\ \mathtt{Percentage\ =\ 84\%}

Hence, **Rachel scored 84% of marks in Grade 8 examination**.

**(03)** Rohit own 70 acres of total land. He decided to use 15 acre of land for agriculture cultivation. Calculate the percentage of land used for agriculture.

**Solution**

Land used for agriculture = 15 acre

Total land = 70 acre

\mathtt{Percentage\ =\frac{Land\ used\ }{Total\ land} \times 100}\\\ \\ \mathtt{Percentage=\ \frac{15}{70} \times 100}\\\ \\ \mathtt{Percentage\ =\ 21.4\%}

Hence, **Rohit used 21.4% of total land for agricultural purposes.**