# Calculating decrease in percentage

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%