A fraction with denominator 100 is called percentage. Numerator of that fraction is called rate percent.
* The term percent means per every 100.
* 50 percent means 50 out of 100.
* The symbol % is used to denote percent. Ex: 20%, 35%, 80% etc.
Percent to fraction: To convert percent into fraction, divide the percent by 100.
Fraction to percent: To convert fraction into percent, multiply the fraction by 100.
Increment percent =
Ex: increment % in 5 and 8 is 3/5 × 100 = 60%.
Decrement percent =
Ex. Decrement % in 5 and 8 is 5/8 × 100 = 37.5%.
Some important percent /fractions.
Following rules should be kept in mind for solving the questions on percentage
1. For converting a given percentage into a fraction, divided it by 100 or multiply by
2. For converting a given fraction into a percentage multiply it by 100.
3. For converting one given quantity, say, x as a percentage of another given quantity, say, y find
Note - percentage is never expressed in any unit like rupees or kilos.
4. When there are two articles ‘a’ and ‘b’ in a group and in the ratio of a : b then to express any one article as a percentage of the group, divide the article by the total articles of the group and multiplies the whole by 100.
Percentage of ‘a’ =
And, Percentage of ‘b’ =
Example 4. How many percent is 15 cm of 1 metre?
Note: Both quantities are converted into same unit.
Example 5. A person spent 85% of his monthly income and thereafter saves Rs.360 per month. Find out his total income.
Sol: Suppose his monthly income is Rs. 100
Expenditure = 85% = Rs. 85
Saving = Rs. 100 – 85 = Rs. 15
∴ If saving is Rs. 15 income is Rs. 100
∴ If saving is Rs. 360 income is
= Rs. 2400
Example 6. If a student gets 38 marks out of 50, what is the percentage of his obtained marks?
Sol: Percentage of obtained marks
Example 7. If two numbers are respectively 30% and 40% more then a third number, what percentage is the first of the second?
Sol: Let the third number be 100
∴ First number = 100 + 30% of 100
and Second number = 100 + 40% of 100
∴ Percentage of the first number to the second number to the second number
Example 8. A student scores 20% marks and fails by 30 marks while another student who scores 32% marks, gets 42 marks more than the minimum required pass marks. What are the maximum marks for the examination?
Sol: 32% - 20% = 12%
And 42–(-30) = 72
∴ 12% marks = 72
∴ 100% marks =
Example 9. An engineering student has to secure 50% marks to pas. He gets 163 marks and fails by 37 marks. Find the maximum marks
Sol: Minimum marks required = 163 + 37 = 200
If 50 are the minimum marks then maximum marks = 100
∴ 200 are the minimum marks then maximum marks =