FINDING PERCENT DECREASE

In our day to day life, often we may see the situations where the values will change. 

For example, 

Decrease in price of an item

Discount on sales

Decrease in temperature

In this section, we will learn the decrease of a value in terms of percent. 

That is, we will calculate, how much a value is decreased per hundred. 

For example, a product is originally priced $250. After negotiation, Lily buys it for $225.

The actual decrease in the price of the product is $25. 

Here, the percent decrease is, how much the price is decreased per hundred. 

For $250, Lily gets a decrease of $25.

Find the decrease for $1.

That is,

=  25 / 250

=  0.1

Find the decrease for $100.

That is,

=  0.1 ⋅ 100

=  10

So, for each $100 of the price, Lily gets a decrease of $10. 

This is called percent decrease. 

Therefore, the price of the product is decreased by 10 percent. 

Formula

Here, the original value is the value before decrease.

Examples

Example 1 : 

What is the percent decrease from 80 to 64 ?

Solution :

Step 1 :

Find the amount of change. 

Actual decrease is 

=  80 - 64

=  16

Step 2 : 

Percentage decrease is 

=  (Actual decrease / Original value) ⋅ 100%

=  (16 / 80) ⋅ 100%

=  0.2 ⋅ 100 %

=  20 %

So, the percent decrease from 80 to 64 is 20.

Example 2 : 

Today, the price of a new cell phone is $129. In 2000, the price of a similar cell phone was $240. What is the percent of decrease in the price of a cell phone from 2000 to today ?

Solution :

Step 1 :

Actual decrease is

=  240 - 129

=  111

Step 2 : 

Percentage decrease is 

=  (Actual decrease / Original value) ⋅ 100%

=  (111 / 240) ⋅ 100%

=  46.25%

So, the percent of decrease in the price of a cell phone from 2000 to today is 46.25. 

Example 3 : 

John bought a car for $12,000 in 2010 and sold it for $7200 in 2018. Find the percentage of depreciation. 

Solution :

Amount of depreciation :

=  12000 - 7200

=  $4,800

Percentage of depreciation :

=  (4800 / 12000) ⋅ 100%

=  0.4 ⋅ 100%

=  40%

So, the percentage of depreciation is 40.

Example 4 : 

In last academic year, there were 20 boys and 15 girls. In this academic year, 4 boys and some girls went to the other school. In this academic year, if the strength of the class is 25, then find the percentage decrease in number of girls. 

Solution :

Details of students strength in the last academic year :

No. of boys  =  20

No. of girls  =  15

Total  =  35

Details of students strength in this academic year :

No. of boys  =  20 - 4  =  16

Total  =  25

No. of girls  =  25 - 16  =  9

No. of girls went to the other school : 

=  No. of girls in last year - No. of girls in this year 

=  15 - 9

=  6

Percentage decrease in the number of girls is

=  (6 / 15) ⋅ 100 %

=  (2 / 5) ⋅ 100%

=  40%

So, the percentage decrease in the number of girls in this academic year is 40.

Example 5 : 

Alex sells two products A and B. The cost price of A is $50 and the cost price of B is $70. If A and B are sold at a loss of 10% and 5% respectively, then find the loss percentage in all (Round your answer to the nearest hundredths). 

Solution :

Given : A is sold at a loss of 10%.

Then, the loss on selling the product A is

=  0.1 ⋅ 50

=  $5

Given : B is sold at a loss of 5%.

Then, the loss on selling the product B is

=  0.05 ⋅ 70

=  $3.5

Therefore, the total loss is 

=  5 + 3.5

=  $8.5

The total cost of the products A and B is 

=  50 + 70

=  120

The loss percentage in all is 

=  (8.5 / 120) ⋅ 100%

≈  7.08%

On selling the products A and B, the loss percentage in all is about 7.08.

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