### percentage

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## Percentage

Definition
Percent means for every 100

So, when percent is calculated for any value, it means that we calculate the value for every 100 of the reference value.
Percent is denoted by the symbol %. For example, x percent is denoted by x%
x% =
100
x

Example : 25% = 25/100 = 14

To express
y
x
as a percent,we have
y
x
=
y
x
* 100%
Formulae :

1. A is what percentage of B
B
A
* 100
2. A is how much percent greater than B
B
A - B
* 100

3. A is how much percent less than B
B
B - A
* 100
4. If A is increased by K% then the new number is
(100+K)% * A
5. If A is decreased by K% then the new number is
(100 - K)% * A

6. If several percentages are acting on the same number then we can add all the percentages.
x1%(K) + x2%(K) + x3%(K) ... = (x1 + x2 + x3...) % (K)

7. If a number K got increased by A% and B% successively then the final percentage is given by

(A + B + AB / 100)%

8. If the price of a commodity increases by R%, the reduction in consumptionso as not to increase the expenditure =

(100 + R)
R
* 100 %

9. If the price of a commodity decreases by R%, the increase in consumptionso as not to decrease the expenditure =

(100 - R)
R
* 100 %

10. If the population of a town = P and it increases at the rate of R% per annum, thenPopulation after n years =

P * ( 1 +
100
R
)n

11. If the population of a town = P and it increases at the rate of R% per annum, thenPopulation before n years =

(1 + R/100)n
P

12. If the present value of a machine = P and it depreciates at the rate of R% per annum, ThenValue of the machine after n years =
P * ( 1 -
100
R
)n

13. If the present value of a machine = P and it depreciates at the rate of R% per annum, ThenValue of the machine before n years =
(1 - R/100)n
P