Percentage
The word percentage means per hundred. For instance, if a person saves 15% of his salary, he is said to save 15 parts out of 100 parts. Which can also be written as (15 / 100).
Information conveyed in percentage does not give the exact but gives as an approximation. The Percentage is commonly used to present data in graphs and tables.
The definition and utility of percentage can be made clear with the help of examples and further discussion in the following paragraphs.
How to convert any Fraction to percentage and vice versa
To convert any faction a / b to rate percentage, multiply it by 100 and put % sign.
Alternatively, to convert a rate percent to a fraction, divide it by 100 and remove the percentage sign.
Example 01 |
Quantity of water in milk constitutes 5 parts of every 20 parts of mixture. What is the percentage of water in the mixture?
Solution:
\[\text{Percentage of water in the mixture}=\left( \frac{5}{20}\times 100 \right)\%=25\%\]
Percentage Increase & Percentage Decrease
Increase or decrease is always in absolute terms whereas percentage increase/decrease is expressed in percentage terms
Percentage increase/decrease is calculated with respect to the base (Previous) value unless mentioned otherwise. \[\text{Percentage Increase}=\frac{\text{Increase}}{\text{Base value}}\times 100\]\[\text{Percentage Decrease}=\frac{\text{Decrease}}{\text{Base value}}\times 100\]
1. If a quantity increased by r %, then final quantity (after increase) is obtained by \[\text{Final Quantity}=\text{Original Quantity}\times \left( \frac{100+r}{100} \right)\]2. Likewise, if a quantity is decreased by r %, the final quantity (after decrease) is obtained by \[\text{Final Quantity}=\text{Original Quantity}\times \left( \frac{100-r}{100} \right)\]
Example 02 |
If A’s income is 20% more than that of B, then how much percent is B’s income less than that of A?
Solution:
Let the income of B be Rs. 100, then income of A = Rs. 120.
In the question B’s income is being compared with that of A and hence base value to find the percentage decrease will be the income of A,
\[\text{Percentage Decrease}=\frac{\text{Decrease}}{\text{Base value}}\times 100\]
\[=\frac{\left( 120-100 \right)}{120}\times 100=\frac{20}{120}\times 100\]
\[=\frac{50}{3}\%=16\frac{2}{3}\%\]
Successive Increase/ Decrease Percentage
In the case of successive changes appears. All successive changes in percentage (increase or decrease) can be represented as a single percentage.
The resultant percentage can be obtained by \left[ a+b+\frac{ab}{100} \right]\% where a and b show the first and second percentage changes.
Unitary Method |
Mixture |