Percentages

Key Points :

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

 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)

  
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.

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	x 100	%.
		(100 + R)

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