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Quantative Aptitude: Percentage & Its Concepts


Percentage 
Percentage is per-cent 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%
 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
331/3%
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? (CGL-2008)
(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? (CGL-2013)
(a) 25%                               
(b) 50%
(c) 75%                               
(d) 20%
Answer:(d)Let C = 100 then  A = 150 , B = 125
(150-125)/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                    (CGL-2003)
(a) 8000                               (b) 7500
(c) 6000                               (d) 10000
Answer (b) Radha’s total percentage expenditure = (40 + 20 + 10 + 10)% = 80%
Percentage savings = 100-80=20%
Now, 20% of her total salary = 1500
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 de-nominator 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? (CGL-2002)
(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/(1-0.20)=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 (MÇP)=30
\ n (MÈP) = n (M) + n (P) – n (MÇP)
= 65+48-30=83
 Percent of students passed = 83
 Percent of students failed = 17
Or, Student passed only in Math = 65-30 = 35%
Students passed only in Physics = 48 -30 = 18%
total pass = 35 + 18 +30 = 83%
 35 + 18 + 30 = 83%
 Failed = 100-83=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/4-2/100 × 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


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