2. Percentage
The word percent
means “Per
Hundred”
Perce
nt
A percent is a fraction with 100
as denominator in each case.
The symbol % is used to indicate
a percent.
So, x percent Means x
hundredths, written as x%
To express x% as a fraction;
we have x% = 100
x
3. Way to express parts of a whole
Fraction =
Decimal = 0.25
Percent = 25%
Ratio = 1:4
4
1
4. Express percent to
fraction or decimal.
20% = = 0.20
Express decimal to
fraction or percent.
Express fraction to decimal
or percent.
= = 0.25 = 25%
100
20
4
1
100
4
1
%5.0%100
200
1
200
1
1000
5
005.0
Problems of percentage
5. 10 % of 80 is calculated by
30 is what percentage of 120?
Here,
is what percentage of
Problems of percentage
2
1
3
1
8
100
10
80
%25
4
1
100
120
30
100
%
Whole
Part
or
Of
Is
%150%100
1
3
2
1
6. Problems of percentage
? % of 250 is 25?
Let ,
x% of 250 = 25
Then,
10,
250
10025
,
25
100
250
25250
100
xso
xor
x
or
x
Find the missing figures
20% of ? is 60?
Let ,
20% of x = 60
Then,
300,
20
10060
,
60
20
100
,
60
100
20
xso
xor
xor
x
7. Problems of percentage
If certain value p increase by
x% then increased value
= (100+x)% of P
Ex. The price of a book is 400
and if price increase by 25%
then what will be the
increased price of this book.
Sol.
The required price will be
(100+25) % of 400
=
=500
If certain value p decrease by
x% then decreased value
= ( 100-x)% of P
Ex. The price of a fan is 5000
and if price decrease by 20%
then what will be the
decreased price of this Fan.
Sol.
The required price will be
(100-25) % of 5000
=
=3750
400
100
125
5000
100
75
8. Problems of percentage
Percent Change
Ex. The price of cup of coffee increased from 80 cents to
84 cents. By what percent did the price change
Sol.
Let the percent change is x%
The required percent is,
%5100
80
4
80
8084
100
x
x
9. Problems of percentage
Ex. If stereo was marked down by 30% and sold for
$84 .What was the presale price of the stereo?
Sol.
Let , the original value of stereo is x
And the new value of stereo is (100-30)=70
So we can use this formula
120,
8407,
84
100
70
xso
xor
x
10. Problems of percentage
If the price of commodity
increases by R% ,then the
reduction in consumption so
as not to increase the
expenditure is
=
If A is R% more than B then
B is less than A
By
If the price of commodity
decreases by R% ,then the
increase in consumption so
as not to decrease the
expenditure is
=
If A is R% less than B then
B is more than A
By
%100
100
R
R %100
100
R
R
%100
100
R
R
%100
100
R
R
11. Problems of percentage
Ex. If the price of sugar
decreases by 20%, than how
much in percent we have to
increase in consumption if
we want to keep expenditure
same.
Sol
So required percentage will
be ,
Ex. If Aslam’s income is
25% more than that of
Asma’s than by how much in
percent is Asma’s income
less than that of Aslam.
Sol
So required percentage will
be,
%20
%100
)25100(
25
%100
100
R
R
%25
%100
)20100(
20
%100
100
R
R
12. Problems of percentage
Result on population
Let the population of a town be P now and suppose it increase at the rate of
R% per annum , then
Result on the depreciation
Let the present value of a machine be P. suppose it depreciates at the rate of
R % per annum then
n
R
PyearsnafterPopulation
100
1___.1
n
R
P
agoyearsnPopulation
100
1
___.2
n
R
P
agoyearsnmachinetheofValue
100
1
______.2
n
R
PyearsnaftermachinetheofValue
100
1______.1
13. Problems of percentage
Ex. The population of a town is 176400.If it increase at the
rate of 5% per annum ,what will be its population 2 years
hence? what was it 2 years ago?
Sol,
So, Population after 2 years =
So, Population 2 years ago =
n
R
PyearsnafterPopulation
100
1___
194481
100
5
1176400
2
n
R
P
agoyearsnPopulation
100
1
___
160000
100
5
1
176400
2
14. Problems of percentage
Ex. The value of a machine depreciates at the rate of 10% per
annum . If its present value is $162000,what will be its worth
after 2 year ? What was the value of the machine 2 years ago?
Sol.
n
R
PyearsnaftermachinetheofValue
100
1______
n
R
P
agoyearsnmachinetheofValue
100
1
______
131220
100
10
1162000
2
200000
100
5
1
162000
2
So, The value of machine 2 years ago
So, The value of machine after 2 years
15. Problems of percentage
Ex. If Rana sold a book to Roni at 25% losses and Roni
sales that book to Runi at $117 with 30% profit .What
was the purchase value of this book of Rana?
Ans. $120
Ex. If the difference between 20% and 30% of a keyboard
price is $50 ,what is the price of this keyboard?
Ans. $500
Ex. When the price of product was decreased by 10%, the
number of sold increased by 30%. What was the effect
on the total revenue ?
Ans. 17%