All Percentage Formulas in One Place
Table of Content:
All Percentage Formulas in One Place
The word percentage means per hundred. For example, if a person saves 30% of his income, it means he saves 30 parts for every 100 parts he earns.
Example 1
Quantity of water in milk constitutes 5 parts for every 15 parts of the mixture. What is percentage water in the mixture?
Percentage increase or decrease is calculated with respect to the base value unless mentioned otherwise.
\begin{align} \\ & Percentage\: increase\: (or)\: decrease \\ & = \frac{Increase\: or\: decrease}{Base\: value} \times 100 \end{align}Example 2
If A’s income is 25% more than B’s income then by what percentage is B’s income less than A’s?
Let B’s income = 100
A’s income = 100 + 25% of 100 = 125
B’s income is less than A’s income by 25
\begin{align} \\ & Percentage\: increase\: (or)\: decrease \\ & = \frac{Decrease}{Base\: value} \times 100 && \ && \\ & = \frac{25}{125} \times 100 && \ && \\ & = 20 \% && \ && \end{align}Note: Here B’s income is compared with A’s income, So A’s income should be taken as the base value
If a Quantity is increased by x%
, then the final quantity is obtained by multiplying original quantity with
If a quantity is reduced by r%
, then the final quantity is obtained by multiplying original quantity with
Example 2
If the price of petrol is increased by 20% and subsequently by 40%, what is the final price if the original price is Rs. 25?
Note: Use –ve sign in case of percentage reduction
Successive increase or decrease of percentage:
Let ‘a’ be the first percentage change and ‘b’ be the second. The net change is given by
\begin{align} \left[ a + b + \frac{a \times b}{100}\ \right] \% \end{align}