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Jun 24, 2015

CONCEPTS OF PERCENTAGE

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Concepts of Percentage




Concepts of Percentage

Definition of Per Cent:

A Fraction having Denominator 100 is called a Per Cent & is denoted by symbol %.



# To convert the Fraction into Percentage
To convert a fraction into Percentage, multiply the fraction by 100 & put % sign.
For Eg: 4/5 à 4/5 * 100 = 80%

# To convert Percentage into a Fraction
To convert a percentage into a fraction replace the % sign with 1/100 & reduce the fraction to simplest form.
For Eg: 20% à 20/100 = 1/5

# To convert Percentage into Ratio
To convert a percentage into a ratio, first convert the given percentage into a fraction in simplest form & then to a ratio.
For Eg: 25% à 25/100 = 1/4 = 1 : 4

Important Concepts:

       1.      100% of a Number = Number itself
               For eg: 100% of 500 = 500
       2.      50% of a number = Half of the number
              For eg: 50% of 500 = 500/2 = 250
       3.      25% of a number = Quarter(1/4th) of the number or Half of 50% of the number
              For eg: 25% of 500 will be 500/4 or 250/2= 125
       4.      To find the 1% of a number, shift the decimal point by 2 place to the left.
               For eg: 1% of 500 will be 5.00
       5.      To find the 10% of a number, shift the decimal point by 1 place to the left.
              For eg:10% of 500 = 50.0
       6.      5% of the number is half of 10% of a number
              For eg:5% of 500 = 50/2=25
       7.      15% of the number = Sum of 10% and 5% of a number
             For Eg: 15% of 500=(10% of 500)+(5% of 500=50 + 2 =75 


Using the above methods now we can find the percentage of a number easily:

Example:    15% of 400 = ?


Step 1: Split the percentage term into 2 numbers that we can easily find the percentage of. 
                 We can split 15% into 10% and 5%

Step 2: First find 10% of 400 by shifting the decimal point to the left by 1 place.


                i.e 10% of 400=40.0

Step 3: Now find 5% of 400 i.e half of 10% 


                i.e 5% of 400=40/2 = 20

Step 4:  Now add both the results


                  we get, 15%+5%=40 + 20 = 60
                  Therefore, 15% of 400 = 60


Important Formulas:

        1)    Percentage Increase/Decrease:
   
      ·         If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:
= [(R/100+R) * 100]%
      ·         If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:
=[(R/100-R) * 100]%
    
         2)    Population:
        If the Population of a town be P now & it increasing at the rate of R% p.a, then,

·         Population after n years =  P[1+(R/100)]^n  
·         Population n years ago = P[1+(R/100)]^n

        3)     Results on Depreciation

If the present value of a machine is P & it depreciates at the rate of R% per annum. Then:
·         Value of the machine after n years= P[1-(R/100)]^n
·         Value of the machine n years ago= P/[1-(R/100)]^n

        4)    If P is R% more than Q, then Q is less than A by
={ [R/(100+R)]*100}%

        5)    If P is R% less than Q, then Q is more than A by
={ [R/(100-R)]*100}%

Learn the Following Table for Fast calculations:

Fraction
Percentage
1/1
100%
1/2
50%
1/3
33.33%
1/4
25%
1/5
20%
1/6
16.66%
1/7
14.28%
1/8
12.5%
1/9
11.11%
1/10
10%
1/15
6.66%
1/20
5%
1/25
4%
1/30
3.33%
1/40
2.5%
1/50
2%
1/60
1.66%
1/75
1.33%
1/80
1.25%
1/90
1.11%
1/100
1%

By Using this Conversion Table we can convert Fraction into Percentage and Percentage into Fraction easily.

For Eg: To find 3/5 in %?
Solution:  As we have 1/5=20%
then, Multiply both sides by 3
i.e 1/5x3 = 3x20%

Therefore, 3/5 = 60%.







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