Percentage - Important Formulae

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	=	1	.
   	100		5

   To express	a	as a percent: We have,	a	=		a	x 100	%.
   	b		b			b

   Thus,	1	=		1	x 100	%	= 25%.
   	4			4

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	x 100	%
   	(100 + R)

   If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

   	R	x 100	%
   	(100 - R)
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		n
   			100

   2. Population n years ago =	P
   	1 + R n 100

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		n
   			100

   2. Value of the machine n years ago =	P
   	1 - R n 100

   3. If A is R% more than B, then B is less than A by		R	x 100	%.
   		(100 + R)

   4. If A is R% less than B, then B is more than A by

   R

   x 100

   %

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