## Jun 24, 2015

### 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 Ã  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% Ã  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% Ã  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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