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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