# Percentage

I. Simple Formula

If a certain value increases by x % , then increased value = 100+ x % of p .

If a certain value decreases by x % , then decreased value = 100- x % of p .

II. 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 years ago =   P/{ 1+( R/ 100)}n

III. 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

Example 1 20%= 20/ 100 = 1 5 ;

Example 2 . 48%= 48/ 100 = 12/ 25 ,  etc

Example 3.   1/ = ( 1/ 4 ×100) % = 25%

Example 4.   0.6 =  6/ 10  3/ = ( 3/ 5 ×100) % = 60%

IV. Increase or decrease in Percentage:

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 %

If A is R% more than B, then B is less than A by { R/( 100- R)} ×100 %

If A is R% less than B, then B is more than A by { R/( 100- R)} ×100 %

V. 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

#### Exercise Percentage

Percentage Formulas

Examples

Exercise 1

Exercise 2