GRE Arithmetic | Percent

Percent is combination of two words per which means for each and cent means hundred. So, percent means some quantity for each hundred quantity. It is denoted by %.

Let’s take a very familiar example in many people’s lives, as we started our education journey we were countered with the question like how many percent marks you have secured in the exam?

Here is the answer to the above question:
There is an exam of 100 marks which have a number of different questions. You attempt the exam and secured 95 marks out of 100 marks. Now convert it into the percentage, as per percent definition 95 marks are for 100 marks or 95% marks. But what if the exam was not of 100 marks? It can be less than 100 or greater than 100 marks. Don’t worry there is a solution for these type of problems too.



Example-1:
If marks of the exam are less than 100. A student secured 35 marks out of 50 marks then what % of marks student secured?
Solution:

= (Marks secured by student / Total marks of the exam) * 100 
= % of marks student secured.
= (35 / 50) * 100
= (7 / 10) * 100
= 70% 

Alternative explanation:
Write down the marks secured per total marks or 35 / 50.

Now convert the denominator into 100.
To convert 50 into 100 it needs to be multiplied by 2.
Since 2 is multiplied in the denominator there is a need to
multiply the numerator by 2 also otherwise it will be unbalanced.

= (35 * 2) / (50  * 2)  
= 70 / 100 

According to basic definition 70 per 100 is 70%

Example-2:
If total marks of the exam are greater than 100. An applicant secured 160 marks in an entrance exam of 200 marks then what % of marks student secured?
Solution:

= (Marks secured by student / Total marks of the exam) * 100 
= % of marks student secured.
= (160 / 200) * 100
= (8 / 10) * 100
= 80% 

Alternative explanation:
Write down the marks secured per total marks or 160 / 200
Now convert the denominator into 100.
To convert 200 into 100 it needs to be divided by 2.
Since the denominator is divided by 2 there is a need to
divide the numerator by 2 also otherwise it will be unbalanced.

= (160 / 2) / (200 / 2)  
= 80 / 100 

According to basic definition 80 per 100 is 80%

Now have some daily life example of percent:

  1. If there is 30% discount on $500 article then what is the cost of article?
    Solution:
    30% is 30 per 100 then 30% of 500 will be

    = (30 / 100) * 500 
    = 150 
  2. Price of an article is increased by 30%, its original price was $300 then what will be the new price?
    Solution:


    30% of 300 = (30 / 100) * 300 = 90 

    New price will be old price + %increased price

    $300 + $90 = $390 
  3. 6 is 30% of what number?
    Solution:
    Let the number is x then 30% of x is 6,

    or 30% of x = 6
    or (30 / 100) * x = 6
    x = 6 / 0.3
    = 20 
  4. Petrol price are hiked by 2.5%, previously it was $0.6 per liter. What is the new petrol rate per liter?
    Solution:

    = 2.5% of 0.6 
    = 0.015
    New price = old price + %increased price
    = 0.6 + 0.015
    = $0.615 

Notes: (change in %)

((Final value  - initial value) / Initial value) * 100 
  • If (Final value – initial value) is negative then % decrease.
  • If (Final value – initial value) is positive then % increase.

For example:

  1. What is the % change if new price of a four-wheeler is $5.5 thousand and it old price was $5.
    Solution:

    = ((Final value  - initial value) / Initial value) * 100 
    = [(5.5 - 5) / 5] * 100
    = .5 / 5 * 100 
    = 10% increase.
     
    ((Final value  - initial value) is positive). 
  2. What is the % change if an energy drink is sold for $15 instead of its original price of $18?
    Solution:

    = ((Final value  - initial value) / Initial value) * 100 
    = [(15 - 18) / 18] * 100
    = (-3 / 18) * 100
    = -100 / 6
    = 16.67% decreased
    
    ((Final value  - initial value) is negative). 


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