Percentage
Percentage is percent which
means parts per hundred
Percent
sign
The percent sign is the
symbol: %
It is written to the right side
of the number: 50%
Percentage
Definition
Percentage is a value that
represents the proportion of one number to another number.
1 percent represents 1/100
fraction.
If we have to convert percentage into fraction
than it is divide by 100.
Example 1 : if we write 45% then its equal to 45/100 or in
fraction 9/20 or in decimal 0.45
if we have to convert fraction into percentage we have to multiple with 100.
Example 2 : if we write 3/5 in fraction it is equal to 60%
if we have to convert fraction into percentage we have to multiple with 100.
Example 2 : if we write 3/5 in fraction it is equal to 60%
3/5x100=60.
Convert Percentage
into Decimal:
20% = 20/100 = 0.5
Convert Decimal Into Percentage:
0.25 = (0.25 × 100)% = 25%
1.50 = (1.50 × 100)% = 150%
Here is a
table of commonly used values shown in Percent, Decimal and Fraction form:
Percent

Decimal

Fraction

1%

0.01

^{1}/_{100}

5%

0.05

^{1}/_{20}

10%

0.1

^{1}/_{10}

12½%

0.125

^{1}/_{8}

20%

0.2

^{1}/_{5}

25%

0.25

^{1}/_{4}

33^{1}/_{3}%

0.333...

^{1}/_{3}

50%

0.5

^{1}/_{2}

75%

0.75

^{3}/_{4}

80%

0.8

^{4}/_{5}

90%

0.9

^{9}/_{10}

99%

0.99

^{99}/_{100}

100%

1


125%

1.25

^{5}/_{4}

150%

1.5

^{3}/_{2}

200%

2

Type
of question that has been always asked
in the exams.
Type : 1: 65g is what per cent of 2
kg? (CGL2008)
(a) 13/4 (b) 35/2
(c) 15/8 (d) 13/8
Answer (a) Required percentage =
(65/2000) ×100=13/4
Type : 2: If 90% of A =30% of B and
B=x% of A, then the value of x is ( CGL – 2011)
(a) 800 (b) 300
(c) 700 (d) 400
Answer: (b) A × 90/100=(B×30)/100
A x 3 = B
A x x% = A x 3
x/100=3 =x=300
Type :3: Given A is 50% larger than C and B is 25%
larger than C, the A is what percent larger than B? (CGL2013)
(a) 25%
(b) 50%
(c) 75%
(d) 20%
Answer:(d)Let C = 100 then A = 150 , B = 125
(150125)/125×100=20%
Type : 4:
Radha spends 40% of her salary on food, 20% on house rent, 10% on
entertainment and 10% on conveyance. If her savings at the end of a month are
Rs. 1500, the her salary per month (in Rs.) is (CGL2003)
(a) 8000 (b) 7500
(c) 6000 (d) 10000
Answer (b) Radha’s total percentage
expenditure = (40 + 20 + 10 + 10)% = 80%
Percentage
savings = 10080=20%
Now, 20% of
her total salary = 1500
So, 1% of her salary will be = 1500 / 20 = 75.
Hence her salary = 100% = Rs 7500
So, 1% of her salary will be = 1500 / 20 = 75.
Hence her salary = 100% = Rs 7500
Type5: If the numerator of a fraction is
increased by 20% and the denominator is decreased by 5%, the value of the new
fraction becomes 5/2. The
original fraction is (CGL – 2005)
(a) 24/19 (b) 3/18
(c) 95/48 (d) 48/95
Answer: (c) Let original fraction by
x/y
According to the question,
(120/100 x)/(95y/100)=5/2
=120x/95y=5/2
x/y=5/2 × 95/120=95/48
Her total salary = (1500×100)/20
= Rs. 7500
Type6: Two numbers are respectively 20%
and 50% of a third number. What percent is the first number of the second? (CGL2002)
(a) 10% (b) 20%
(c) 30% (d) 40%
Answer: d) Let the third number be x,
According to the questions:
First number = 20/100 × x=x/5
Second number = 50/100 × x=x/2
Required percentage
= (x/5×100)/(x/2) =x/5×2/x×100 =
40%
Type 7: A reduction of 20% in the price
of oranges enables a man to buy 5 oranges more for Rs. 10/. The price of an
orange before reduction was: ( CGL – 2000)
(a) 20 paise (b) 40 paise
(c) 50 pasie
(d) 60 pasie
Answers: (c) 20% of Rs. 10 = 20/100 ×Rs.10=Rs.2
Reduced
price of 5 oranges = Rs. 2
Reduced
price of 1 orange = (Rs.2)/5=200/5
paise = 40 paise
Original
price of 1 orange =
40/(10.20)=40/0.8=400/8 = 50 paise
Type8: In an examination, 65% of the
students passed in Mathematics, 48% passed in Physics and 30% passed in both.
How much per cent of students failed in both the subjects? (CGL 2007)
(a) 17% (b) 43%
(c) 13% (d) 47%
Answer: (a) n (M) = 65, n (P) = 48, n
(MÃ‡P)=30
\ n (MÃˆP) = n (M) + n (P) – n (MÃ‡P)
=
65+4830=83
Percent of students passed = 83
Percent of students failed = 17
Or, Student
passed only in Math = 6530 = 35%
Students
passed only in Physics = 48 30 = 18%
total pass =
35 + 18 +30 = 83%
35 + 18 + 30 = 83%
Failed = 10083=17%
Type 9: A number is increased by 20% and
then it is decreased by 10%. Find the net increase or decrease per cent.
(a) 10%
increase (b) 10% decrease
(c) 8%
increase (d) 8% decrease
Answers: (c) Net %
change = A + B + AB/100
Here, A =
20%, B =  10%
Net % change = 20 – 10 – 200/100 = 10 – 2 = 8% +ve sign shows increase
Type10: In an
election between two candidates, 75% of the voters cast their votes, out of
which 2% votes were declared invalid. A candidate got 9261 votes which were 75%
of the valid votes. The total number of voters enrolled in that election was ( CGL – 2003)
(a) 16000 (b) 16400
(c) 16800 (d) 18000
Answer (c) Let the
total number of voters enrolled be x.
Number of
votes polled = 75% of x = 3x/4
= 3x/42/100
× 3x/4=3x/4*3x/200=147x/200
Now, 75% of
147x/200=9261
Or, 3/4 of
147x/200 = 9261
Or, x =
(926×4×200)/(3×147)=16800