In this chapter, we will learn to calculate the percentage decrease of given numbers.

Apart from the method, some solved examples are also given for better understanding of the concept.

## Find percentage decrease in values

We will understand the concept with the help of example.

Let the price of toy decreased from 100$ to 90$.

The** percentage decrease in value can be calculated using the following steps**;

**(a) Find the decrease in value.**

⟹ 100 – 90

⟹ 10 $

In this example, the value has been decreased by 10$.**(b) Now apply the following formula;**

\mathtt{\%\ decrease\ =\frac{Decrease\ in\ value}{Initial\ value} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ \ \frac{10}{100} \times 100}\\\ \\ \mathtt{\%\ decrease=\ 10\%\ }

Hence, the value has been decrease by 10%.

Using the above two steps, you can calculate the % decrease in value of any given number.

Given below are some solved examples for better understanding.

### Percentage decrease calculation – Solved examples

**Example 01**

The Price of Honda car decreased from 20,000$ to 18,500$. Find the price reduction in percentage.

**Solution**

Initial Price = 20,000 $

Final Price = 18,500 $

Price reduction = 20,000 – 18,500 = $ 1500

The percentage decrease in value can be calculated using following formula;

\mathtt{\%\ decrease\ =\frac{Decrease\ in\ price}{Initial\ price} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ \ \frac{1500}{20000} \times 100}\\\ \\ \mathtt{\%\ decrease=\ 7.5\%}

Hence, **the price of car is decreased by 7.5%**

**Example 02**

The population of town in USA decreased from 50,000 to 45,000. Calculate the % decrease in population.

**Solution**

Initial Population : 50,000

Final Population : 45,000

Decrease in population = 50,000 – 45,000 = 5000

The percentage decrease in population can be calculated as follows;

\mathtt{\%\ decrease\ =\frac{Decrease\ in\ population}{Initial\ population} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ \ \frac{5000}{50000} \times 100}\\\ \\ \mathtt{\%\ decrease=\ 10\%}

Hence,** the population decreased by 10%**

**Example 03**

Matt scored 60 marks in test 01. In test 02, he scored 33 marks. Calculate the % decrease in marks.

**Solution**

Initial score = 60

Final score = 33

Decrease in score = 60 – 33 = 27

The % decrease in marks can be calculated as follows;

\mathtt{\%\ decrease\ =\frac{Decrease\ in\ marks}{Initial\ marks} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ \ \frac{27}{60} \times 100}\\\ \\ \mathtt{\%\ decrease=\ 45\%}

Hence, **Matt score has been decreased by 45%.**

**Example 04**

After joining weight loss program, John reduced his weight from 85 kg to 70 Kg. Calculate the % decrease in weight.

**Solution**

Initial weight = 85 kg

Final weight = 70 kg

Decrease in weight = 85 – 70 = 15 kg

The percentage decrease in weight is calculated as follows;

\mathtt{\%\ decrease\ =\frac{Decrease\ in\ weight}{Initial\ weight} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ \ \frac{15}{85} \times 100}\\\ \\ \mathtt{\%\ decrease=\ 17.65\%}

Hence, **the weight has been decreased by 17.65%**

**Example 05**

The price of toy decreased from 7$ to 5$. Calculate the % decrease in price.

**Solution**

Initial Price = 7$

Final Price = 5 $

Decrease in Price = 7 – 5 = 2$

The % decrease in price is calculated as follows;

\mathtt{\%\ decrease\ =\frac{Decrease\ in\ price}{Initial\ price} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ \ \frac{2}{7} \times 100}\\\ \\ \mathtt{\%\ decrease=\ 28.57\%}

Hence,** price has been reduced by 28.57%**

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

## Percentage decrease – Solved Problems

**(01) Calculate the percentage decrease of below questions**

(a) Original number = 20

Final number = 12

(b) Original number = 75

Final number = 60

(c) Original number = 13

Final number = 9

(d) Original number = 27

Final number = 15

(e) Original number = 45

Final number = 40

**(a)** Original number = 20

Final number = 12

\mathtt{\%\ decrease\ =\ \ \frac{20-12}{20} \times 100}\\\ \\ \mathtt{\%\ decrease=\ \frac{8}{20} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ 40\%}

**The value has been decreased by 40%**

**(b)** Original number = 75

Final number = 60

\mathtt{\%\ decrease\ =\ \ \frac{75-60}{75} \times 100}\\\ \\ \mathtt{\%\ decrease=\ \frac{15}{75} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ 20\%}

**The value has been decreased by 20%**

**(c)** Original number = 13

Final number = 9

\mathtt{\%\ decrease\ =\ \ \frac{13-9}{13} \times 100}\\\ \\ \mathtt{\%\ decrease=\ \frac{4}{13} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ 30.77\%}

**The value has been decreased by 30.77%**

**(d) **Original number = 27

Final number = 15

\mathtt{\%\ decrease\ =\ \ \frac{27-15}{27} \times 100}\\\ \\ \mathtt{\%\ decrease=\ \frac{12}{27} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ 44.44\%}

**Value has been decreased by 44.44%**

**(e) **Original number = 45

Final number = 40

\mathtt{\%\ decrease\ =\ \ \frac{45-40}{45} \times 100}\\\ \\ \mathtt{\%\ decrease=\ \frac{5}{45} \times 100}\\\ \\ \mathtt{\%\ decrease\ =\ 11.11\%}

Hence, **value has been decreased by 11.11%**