Percentage
Key facts
- Percentage means "per hundred", so 25% equals 25/100, 1/4, and 0.25 in the same value system.
- The Census of India 2011 recorded Rajasthan's population as 6,85,48,437, making percentage growth and share calculations natural data-interpretation e...
- Rajasthan's official area is 3,42,239 sq km, so area-share questions need a fixed base before any percentage is computed.
- India introduced Goods and Services Tax on 1 July 2017, and tax questions normally apply a percentage rate to the taxable value stated in the problem.
- Successive percentage change uses the revised base after every step; +20% followed by -10% gives a net +8%, not +10%.
Key Points at a Glance
- 1
Percentage means "per hundred", so 25% equals 25/100, 1/4, and 0.25 in the same value system.
- 2
The Census of India 2011 recorded Rajasthan's population as 6,85,48,437, making percentage growth and share calculations natural data-interpretation examples.
- 3
Rajasthan's official area is 3,42,239 sq km, so area-share questions need a fixed base before any percentage is computed.
- 4
India introduced Goods and Services Tax on 1 July 2017, and tax questions normally apply a percentage rate to the taxable value stated in the problem.
- 5
Successive percentage change uses the revised base after every step; +20% followed by -10% gives a net +8%, not +10%.
- 6
Profit and loss percentages are measured on cost price, while discount percentage is measured on marked price.
- 7
Simple interest grows linearly with time, but compound interest changes the base after each compounding period.
- 8
In data interpretation, percentage change is always change divided by original value, then multiplied by 100.
Continue studying
Meaning, Fractions and Decimal Conversion
Percentage is a compact way to compare a part with a base of 100. If 36 out of 80 candidates qualify in a mock test, the qualifying percentage is 36/80 x 100 = 45%. The numerator is the part being measured, the denominator is the total base, and the multiplication by 100 only changes the form of expression. The value does not change when 45% is written as 45/100, 9/20, or 0.45.
Fast conversion saves time in CET arithmetic. The most useful pairs are 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/8 = 12.5%, 1/10 = 10%, 1/12 = 8.33%, 1/16 = 6.25%, 1/20 = 5%, and 1/25 = 4%. These are not separate facts; they are the same division written in three forms. For example, 3/8 = 0.375 = 37.5%, so a 37.5% question can often be solved as a simple fraction question.
Exam use: convert the format that looks difficult into the format that gives the shortest arithmetic.
Open the complete note
This public page shows the first available section. The study pack opens the complete topic with all revision material.
6 more sections in the complete note
Open study pack