FINDING PERCENT DECREASE WORKSHEET

Problem 1 : 

What is the percent decrease from 80 to 64 ?

Problem 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 ?

Problem 3 : 

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

Problem 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. 

Problem 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). 

Detailed Answer Key

Problem 1 : 

What is the percent decrease from 80 to 64 ?

Solution :

Step 1 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  80 - 64

=  16

Step 2 : 

Percentage change is 

=  (Amount of change / Original amount)  100 %

=  (16 / 80) ⋅ 100%

=  0.2 ⋅ 100 %

=  20 %

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

Problem 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 :

Find the amount of change. 

Amount of change  =  Greater value - Lesser value 

=  240 - 129

=  111

Step 2 : 

Percentage change is 

=  (Amount of change / Original amount)  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. 

Problem 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.

Problem 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.

Problem 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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