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Theory and Formula for Percentage

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 percent we have
a/b
= (
a/b
x 100)%

Thus ,
1/4
= (
1/4
x 100 )% = 25%
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]%
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 =n [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


x is what percent of y = (
x/y
x 100)%
x is what percent greater than y = (
x - y/y
x 100)%
x is what percent lesser than y = (
y - x/y
x 100)%
If each of side of a rectangle or any two dimensional shape is increased by x%, its area is increased by = (
x2/100
+ 2x)%

If radius of a circle is increased by x%, its area is increased by (
x2/100
+ 2x)%
Suppose a number is increased by x% and then again increased by y%.

Then, net change = (x + y +
xy/100
)%

For decrease, use negative sign. Thus, we get the following formulas as well.

Suppose a number is decreased by x% and then again decreased by y%

Then, net change = (-x - y -
xy/100
)%

Suppose a number is increased by x % and then decreased by y % .

Then, net change = (x - y -
xy/100
)%