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PERCENTAGE

        A fraction with denominator 100 is called percentage. Numerator of that fraction is called rate percent.

The term percent means per every 100.

50 percent means 50 out of 100.

The symbol  % is used to denote percent. Ex: 20%, 35%, 80% etc.

Percent to fraction: To convert percent into fraction, divide the percent by 100.

                                   

Fraction to percent: To convert fraction into percent, multiply the fraction by 100.

                    

              Increment percent = 

       Ex: increment % in 5 and 8  is  3/5  × 100 = 60%.

             Decrement percent  =  

Ex. Decrement % in 5 and 8 is 5/8  × 100 = 37.5%. 

Some important percent /fractions.

 


 Following rules should be kept in mind for solving the questions on percentage —
1. For converting a given percentage into a fraction, divided it by 100 or multiply by 1/100 
2. For converting a given fraction into a percentage multiply it by 100.
3. For converting one given quantity, say, x as a percentage of another given quantity, say, y find  x/y*100.
   Note - percentage is never expressed in any unit like rupees or kilos.
4. When there are two articles ‘a’ and ‘b’ in a group and in the ratio of a : b then to express any one article as a percentage of the group, divide the article by the total articles of the group and multiplies the whole by 100.
           Percentage of ‘a’ = 
             And, Percentage of ‘b’ = 

 

EXAMPLES
 

Example 4. How many percent is 15 cm of 1 metre?

  Note: Both quantities are converted into same unit.
 

Example 5.  A person spent 85% of his monthly income and thereafter saves Rs.360 per month. Find out his total income.
Sol: Suppose his monthly income is Rs. 100
             Expenditure = 85% = Rs. 85
             Saving = Rs. 100 – 85 = Rs. 15
       ∴  If saving is Rs. 15 income is Rs. 100
       ∴  If saving is Rs. 360 income is  =100*360/15
                                                                  = Rs. 2400
Example 6. If a student gets 38 marks out of 50, what is the percentage of his obtained marks?
Sol:  Percentage of obtained marks  =38/50*10
                                                                = 76%

 

Example 7.  If two numbers are respectively 30% and 40% more then a third number, what percentage is the first of the second?
Sol: Let the third number be 100
         ∴ First number  = 100 + 30% of 100
                                       = 130
 and Second number   = 100 + 40% of 100
                                       = 140
 ∴ Percentage of the first number to the second number to the second number 
            

Example 8. A student scores 20% marks and fails by 30 marks while another student who scores 32% marks, gets 42 marks more than the minimum required pass marks. What are the maximum marks for the examination?
Sol:   32% - 20% = 12%
      And 42–(-30) = 72
      ∴ 12% marks = 72          
   ∴ 100% marks = 72*100/12=600

 

Example 9.  An engineering student has to secure 50% marks to pas. He gets 163 marks and fails by 37 marks. Find the maximum marks
Sol: Minimum marks required = 163 + 37  = 200
         If 50 are the minimum marks then maximum marks  = 100
  ∴  200 are the minimum marks then maximum marks = 100*200/50=400

Posted Date : 20-08-2021

 

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