What is percentage ?
The word ‘per cent’ means per hundred, Thus x per cent means x parts out of 100 parts, this can also be written as . Therefore per cent is a fraction whose denominator is 100, and numerator of this fraction is called as rate per cent. Here x per cent is the rate and is denoted by the symbol %
Quick List of Formulae
- Any fraction if multiplied by 100 converts to a percentage (%)
- a % of any number b =
- a is what % of b means
- similarly, b is what % of a means
- If a number N increases by x% then it becomes but if N decreases by x% it becomes
- If a number or quantity N1 becomes N2 then percentage change = =
- if % change is (+) positive then it is % Increase and if % change is (-) negative then it is % decrease
- If a number changes by x% and then by y% the net change in % is =
- If A is x% more than B, then B is =
- If A is x% less than B, then B is =
1. Fraction to Rate Per Cent
To convert any fraction to Rate Per Cent we need to multiply the fraction by 100 and put % sign.
2. Rate Per Cent of a Number
Rate per cent of a number is the product of equivallent fraction and the number.
value of rate percent =
Example 1: 25% of 1000 = = 250
Example 2: 9% of what number is 36 =
3. Expressing a given quantity as a percentage of another given quantity
x is what % of y ?
This question requires us to express one given quantity ‘x‘ as percentage of another given quantity ‘y‘ since ‘y‘ is the basis of comparison, so, ‘y‘ will be the denominator. hence the required percentage is =
Example 1 : 30 is what percentage of 150 or what percentage of 150 is 30 ?
Here, x = 30 ; y = 150 Therefore, =
Example 2: What % of 320 is 128
Here, 320 is the basis of comparison so 320 will be the denominator, therefore, the required percentage = .
4. Percentage Change
If a number or quantity increases or decreases to a new number then, % increase or decrease = Here, original value means the value of the number before increase or decrease.
Example: A man invested ₹64,000 and ₹80,000 respectively in the year 2018 and 2019. What is the percentage increase in the year 2019 from the previous year?
Solution: Required % increase = =
5. Percentage Change and New Number
If a number is increased by x% then, New Number = Similarly, if a number is decreased by x% then, New Number =
Example: The Current salary of a person is ₹30000 & it has to be increased by 20% from next year. What will be the increased salary of the person ?
Solution: Here the salary increase = 20% therefore x= 20 according to our formula % increase = = Hence the new salary will be ₹36000
6. Two Step Change of Percentage
If a number is changed by x% in the first step and again changed by y% in the next step then the net change in percentage of the original number is If there is a decrease in any step then put a Minus (-) sign before the number. And if the total change is Negative (-) then the resultant number is decreased. and if it’s positive then the final change is Increased.
Example: If a number is increased by 20% and then decreased by 10% find the net change in the number.
Solution: Net change = Therefore, x = 20, & y = -10 According to our formula: So the final increase will be 8% as our final result is positive there will be a net increase in the original number.
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