In this chapter, we will learn to calculate the increase in value using the percentage.

Here we will discuss the method to calculate the increase in percentage value along with examples.

At the end of the chapter, some problems are also given for your practice.

## Find increase in value using percentage

We will understand the concept with the helps of example.

Let the **price of chips increased from 5$ to 7$**.

The percentage increase in price is calculated by using following steps;**(a) Calculate the increase in value**.

⟹ $7 – $5

⟹ $ 2

Here, the price has been increased by 2$.**(b) Apply percentage increase formula**;

\mathtt{Percentage\ increase\ =\frac{Increase\ in\ Value\ }{Original\ Value} \times 100}

Putting the values, we get;

\mathtt{Percentage\ increase\ }\\\ \\ \mathtt{\Longrightarrow \ \ \frac{2\$}{5\$} \times 100}\\\ \\ \mathtt{\Longrightarrow \ 40\%}

The **price of chips has increased by 40%**

Hence, using the above two steps, you can calculate the percentage increase in any given value.

**Note:**

The numerator and denominator in above formula should be in same format. For example, if numerator value is in dollars then denominator value should also be in dollars otherwise we will get faulty results.

Given below are some solved examples for further clarity.

### Percent increase – Solved examples

**Example 01**

Susan weight increased from 60 kg to 75 kg. Calculate the % increase in weight.

**Solution**

Increase in weight = 75 – 60 = 15

\mathtt{\%\ increase\ \ =\ \ \frac{15}{60} \times 100}\\\ \\ \mathtt{\%\ increase\ =\ 25\%}

Hence, **Susan’s weight has been increased by 25%.**

**Example 02**

The population of town in USA increased from 50,000 to 52,000. Calculate the percentage increase in population.**Solution**

Original population = 50,000

New population = 52,000

Increase in population = 52,000 – 50,000 = 2000

\mathtt{\%\ increase\ =\frac{Increase\ in\ population\ }{Original\ population} \times 100}\\\ \\ \mathtt{\%\ increase\ \ =\ \ \frac{2000}{50000} \times 100}\\\ \\ \mathtt{\%\ increase\ =\ 4\%}

Hence, **population of town is increased by 4%**

**Example 03**

The price of Honda Accord is $23,000. After two years, the company increased the price to $25000. Calculate the percent increase in price.

**Solution**

Original Price = $23,000

Final Price = $ 25,000

Increase in Price = 25000- 23000 = $ 2000

The percentage increase is calculated by using following formula;

\mathtt{\%\ increase\ =\frac{Increase\ in\ price\ }{Original\ price} \times 100}\\\ \\ \mathtt{\%\ increase\ \ =\ \ \frac{2000}{23000} \times 100}\\\ \\ \mathtt{\%\ increase\ =\ 8.69\%}

Hence, **the price of the car is increased by 8.69%**

**Example 04**

The height of a plant is 4 meters. After six months, the height is now increased to 7 meters. Calculate the % increase in height.

**Solution**

Original height = 4 meter

New height = 7 meter

Increase in height = 7 – 4 = 3 meter.

To calculate the percentage increase, do the following calculation;

\mathtt{\%\ increase\ =\frac{Increase\ in\ height\ }{Original\ height} \times 100}\\\ \\ \mathtt{\%\ increase\ \ =\ \ \frac{3}{4} \times 100}\\\ \\ \mathtt{\%\ increase\ =\ 75\%}

Hence, **height of plant is increased by 75%.**

**Example 05**

The price of candy is 10$. The company has decided to increase price by 40%. Calculate the final price.

**Solution**

Initial Price = 10$

Price increased by 40%.

Let the final price be x$

Use the following formula to calculate the final price.

\mathtt{\%\ increase\ =\frac{Final\ Price-\ Initial\ Price\ }{Initial\ Price} \times 100}\\\ \\ \mathtt{40\ =\ \ \frac{x-10}{10} \times 100}\\\ \\ \mathtt{\frac{40\times 10}{100} =\ x-10}\\\ \\ \mathtt{4\ =\ x-10}\\\ \\ \mathtt{x\ =\ 14}

Hence,** the final price of candy is 14$**

I hope you understood the above examples. Given below are some problems for your practice.

## Percent increase – Solved problems

(01) Calculate the percent increase of below questions.

(a) Original number : 23

Final number : 50

(b) Original number : 100

Final number : 106

(c) Original number : 21

Final number : 25

(d) Original number : 80

Final number 100

(e) Original number 10

Final number 90

Solution**(a)** Original number : 23

Final number : 50

\mathtt{\%\ increase\ =\ \ \frac{50-23}{23} \times 100}\\\ \\ \mathtt{\%\ increase=\ \frac{27}{23} \times 100}\\\ \\ \mathtt{\%\ increase=\ 117.4\%\ }

**The number has been increased by 117.4%**

**(b) **Original number : 100

Final number : 106

\mathtt{\%\ increase\ =\ \ \frac{106-100}{100} \times 100}\\\ \\ \mathtt{\%\ increase=\ \frac{6}{100} \times 100}\\\ \\ \mathtt{\%\ increase=\ 6\%\ }

Hence, **the number has been increased by 6%**

**(c)** Original number : 21

Final number : 25

\mathtt{\%\ increase\ =\ \ \frac{25-21}{21} \times 100}\\\ \\ \mathtt{\%\ increase=\ \frac{4}{21} \times 100}\\\ \\ \mathtt{\%\ increase=\ 19.04\%\ }

Hence, **number has been increased by 19.04%**

**(d) **Original number : 80

Final number 100

\mathtt{\%\ increase\ =\ \ \frac{100-80}{80} \times 100}\\\ \\ \mathtt{\%\ increase=\ \frac{20}{80} \times 100}\\\ \\ \mathtt{\%\ increase=\ 25\%\ }\

Hence, **number has been increased by 25%.**

**(e)** Original number 10

Final number 90

\mathtt{\%\ increase\ =\ \ \frac{90-10}{10} \times 100}\\\ \\ \mathtt{\%\ increase=\ \frac{80}{10} \times 100}\\\ \\ \mathtt{\%\ increase=\ 800\%\ }

Hence, **the number has been increased by 800%**

**(02)** The weight of a man increased from 80 kg to 85 kg. Find the % increase in weight.

**Solution**

Original weight = 80 Kg

Final weight = 85 Kg

Increased weight = 85 – 80 = 5 kg

The percentage increase is calculated by following formula;

\mathtt{\%\ increase\ =\frac{Final\ -Initial\ weight}{Initial\ weight} \times 100}\\\ \\ \mathtt{\%\ increase\ =\ \ \frac{5}{80} \times 100}\\\ \\ \mathtt{\%\ increase=\ 6.25\%}

The **weight has been increased by 6.25%**