Percentages
All quantitative aptitude examinations will have questions based on percentage system.It is important to know the clear concepts of percentage which plays a very vital role in Data Interpretation besides quantitative aptitude section. Nearly 4-5 % of problems in numberical ability are being asked in CAT every year. In other entrance exams like MAT, XAT,bank exams etc. there are too many questions asked from this chapter. Here we have provided a set of basic concepts, tips and shortcuts on how to solve percentage problems easily and quickly.
The term ‘per cent’ means ‘ for every hundred’. Thus, 50 % means 50 parts out of 100 parts. This can also be written as 50/100. Since percent is a form of fraction , we can express percent as fractions (or decimals) and vice-versa.
Fractional equivalents of Important Percentages
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|
1 |
100 | 200 | 300 | 400 | 500 | 600 | 700 | 800 | 900 | 1000 | 1100 |
1200 |
|
2 |
50 | 100 | 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 | 550 |
600 |
|
3 |
33.33 | 66.66 | 100 | 133.33 | 166.66 | 200 | 233.33 | 266.66 | 300 | 333.33 | 366.60 |
400 |
|
4 |
25 | 50 | 75 | 100 | 125 | 150 | 175 | 200 | 225 | 250 | 275 |
300 |
|
5 |
20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 | 220 | 240 |
| 6 | 16.66 | 33.33 | 50 | 66.66 | 83.33 | 100 | 116.66 | 133.33 | 150 | 166.66 | 183.33 |
200 |
|
7 |
14.28 | 28.56 | 42.85 | 57.13 | 71.42 | 85.71 | 100 | 114.28 | 128.56 | 142.85 | 157.13 | 171.42 |
| 8 | 12.5 | 25 | 37.5 | 50 | 62.5 | 75 | 87.5 | 100 | 112.5 | 125 | 137.5 |
150 |
|
9 |
11.11 | 22.22 | 33 | 44.44 | 55.55 | 66.66 | 77.77 | 88.88 | 100 | 111.11 | 122.22 | 133.33 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 |
120 |
|
11 |
9.09 | 18.18 | 27.27 | 36.36 | 45.45 | 54.54 | 63.63 | 72.72 | 81.81 | 90.9 | 100 | 109.09 |
| 12 | 8.33 | 16.66 | 25 | 33.33 | 41.66 | 50 | 58.33 | 66.66 | 75 | 83.33 | 91.66 |
100 |
|
13 |
7.69 | 15.38 | 23.07 | 30.76 | 38.46 | 46.15 | 53.84 | 61.53 | 69.23 | 76.92 | 84.61 | 92.30 |
| 14 | 7.14 | 14.28 | 21.42 | 28.57 | 35.71 | 42.85 | 50 | 57.14 | 64.28 | 71.42 | 78.57 |
85.71 |
| 15 | 6.66 | 13.33 | 20 | 26.66 | 33.33 | 40 | 46.66 | 53.33 | 60 | 66.66 | 73.33 |
80 |
- Learn the values given in the table so that all these rest on your finger tips.
General Rules
-
Conversion of Percentage into a fraction
To convert a percentage into a fraction, replace the % sign with 1/100 and reduce the fraction to simplest form.
For Example 20% = 20/100 = 1/5
-
Conversion of a percentage into a ratio
To convert a percentage into ratio, first convert the given percentage into fraction in simplest form and then to ratio.
For Example
25% = 25/100 =1/4 = 1: 4
-
Conversion of ratio into a percentage
To convert a ratio into percentage, first convert the given ratio into a fraction then to a percentage.
For Example
1:5 = 1/5 = 1/5 x100 = 20%
-
Conversion of a Percentage into Decimal
To convert a percentage into decimal remove the % sign and move the decimal point twoplaces to the left.
For Example
360% = 3.60
87.9 % = 0.879
-
Conversion of Decimal into a Percentage
To convert a decimal into a percentage, move the decimal point two place to the right (adding zeros if necessary) and put % sign.
For Example
6.89 = 689 %
0.54 = 54%
-
Percentage of Quantity
Let one given quantity be x and another given quantity be y. It is iften asked to find what percentage of y is x. Here both quantities (x and y) should be in same units. If not, they should be converted into the same unit. To find what percent the first number is of second number, we divide the first number by the second number and multiply the result by 100.
Example 1
What percent is number 3 of number 20?
Solution : 3/20x 100 = 15%
Example 2
30 is what percent of 150? or what percentage of 150 is 30 ?
Solution : 30/150 x100 = 20%
Example 3
In a factory of 180 workers, 12 were absent in a day. What percentage was present?
Solution : Present = 180- 12 =168
Percentage presence = 168/159x 100 = 93.33 %
