# Percentages

## 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 66.66 100 133.33 166.66 200 233.33 266.66 300 333.33 366.6 400 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 92.3 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 %

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