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1. Concept of Percentage:
   
  By a certain percent, we mean that many hundredths.
  Thus, x percent means x hundredths, written as x%.
 
To express x% as a fraction: We have, x%
x
100
 
 
Thus, 20% =
20
100
=
1
5
 
 
To express
a
b
 as a percent: We have,
a
b
=  
a
b
 x 100   %    
 
Thus,
1
4
=  
1
4
 x 100   % = 25%    
   
2. 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)
 x 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)
 x 100    %
3. Results on Population:
  Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
 
1. Population after n years = P   1 +
R
100
  n  
 
2. Population n years ago =
P
  1 +
R
100
  n
   
   
4. Results on Depreciation:
  Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
 
1. Value of the machine after n years = P   1 -
R
100
  n  
 
2. Value of the machine n years ago =
P
  1 -
R
100
  n
   
 
3. If A is R% more than B, then B is less than A by  
R
(100 + R)
 x 100    %  
 
4. If A is R% less than B, then B is more than A by  
R
(100 - R)
 x 100    %