HOW TO CALCULATE PERCENTAGES

Percentage can be estimated as follows. 

Comparing the given number to 100

or

Ratio between the given number and 100

or

 Saying per 100

For example, 

30 %  =  30/100  or  30 : 100

If you want to find the percentage of a number, say 'A' in the number B, it can be calculated as follows. 

Percentage of A in B  =  (A/B) ⋅ 100%

If you want to find some percentage of a particular number, the percentage has to multiplied by that number.

For example,

if you want to find y% of the number, say 'A', it can be calculated as follows. 

y% of A  =  (y/)100% ⋅ A

In a business, if there is profit, then profit percent can be calculated as follows. 

Profit percent  =  (Profit / Cost price) ⋅ 100 %

In a business, if there is loss, then loss percent can be calculated as follows. 

Loss percent  =  (Los / Cost price) ⋅ 100 %

In a sale, if there is discount, then loss percent can be calculated as follows. 

Discount percent  =  (Discount amount/ List price) ⋅ 100 %

Example 1 :

Find the percentage of 15 in 60.

Solution :

Percentage of 15 in 60 is

=  (15/60) x 100 %

=  (1/4) x 100 %

=  25 %

Example 2 :

Mr. John bought an item for $90 and sold it for $108. Find the profit. 

Solution :

Profit  =  $108 - $90  =  $18

Profit percentage is

=  ($18/$90) x 100 %

=  (1/5) x 100 %

=  20 %

Example 3 :

The list price of item is $85 and it is sold for $76.5. Find the discount percentage. 

Solution :

Discount  =  $85 - $76.5  =  $8.5

Discount percentage is

=  ($8.5/$85) x 100 %

=  (1/10) x 100 %

=  10 %

Example 4 :

Find the 20% of $50.

Solution :

20% of $50 is

=  20/100 ⋅ 50

=  0.2 ⋅ 50

=  $10

Example 5 :

Find the 50% of $80.

Solution :

50% of $80 is

=  50/100 ⋅ 80

=  0.5 ⋅ 80

=  $40

Example 6 :

Find the 23% of $80.

Solution :

23% of $80 is

=  23/100 ⋅ 80

=  0.23 ⋅ 80

=  18.4

Example 7 :

Find the percent of 20 minutes in 1 hour. 

Solution :

To answer this question, both the given quantities must be in same units.

Here, one of the quantities is in minutes and other one is in hour. 

So, convert 1 hour into minutes.  

1 hour  =  60 minutes

Percent of 20 minutes in 1 hour (60 minutes) is 

=  (20 / 60) ⋅ 100%

≈  33.33%

So, the percent of 20 minutes in 1 hour is about 33.33.

Example 8 :

What percent of 15 inches in 5 feet ? 

Solution :

To answer this question, both the given quantities must be in same units.

Here, one of the quantities is in inches and other one is in feet. 

So, convert 5 feet into inches.  

1 feet  =  12 inches

5 feet  =  5 ⋅ 12 inches

5 feet  =  60 inches

Percent of 15 inches in 1 feet (60 inches) is 

=  (15 / 60) ⋅ 100%

=  25%

So, the percent of 15 inches in 5 feet is 25.

Example 9 :

An item is marked up by 30% and then 10% discount is allowed from the marked up price. Find the profit percentage. 

Solution :

Let $100 be the cost price of the item. 

After 30% mark up, the price of the product is

=  1.3 ⋅ 100

=  $130

After 10% discount, the price of the product is

=  0.9 ⋅ 130

=  $117

So, the selling price of the product is $117.

The cost price of the product is $100 and the selling price is $117.

Percentage increase from 100 to 117 is 17. 

So, the profit percentage is 17.

Example 10 :

An item is sold at a discount of 10% and there is sales tax 10% imposed on the discounted price. The final price is what percentage of the actual price ?

Solution :

Let $100 be the actual price.

The price after 10% discount is 

=  (100 - 10)% of $100

=  90% of $100

=  $90

The Final price (price after sales tax 10% on the discounted price) is 

=  (100 + 10)% of $90

=  110% of $90

=  1.1 ⋅ $90

=  $99

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