All Percentage Formulas in One Place

Rumman Ansari   Software Engineer   2023-03-30   517 Share
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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?

\begin{align} \\ & Percentage\: of\: water \\ & = \frac{Number\: of\: parts\: of\: water}{Number\: of\: parts \: of\: mixture} \\ & = \frac{ 5}{ 15 } \times 100 \\ & = 33.33 \% \end{align}

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

\begin{align} \:\left(\frac{ 100 + x}{100}\right) \end{align}

If a quantity is reduced by r%, then the final quantity is obtained by multiplying original quantity with

\begin{align} \:\left(\frac{ 100 - r}{100}\right) \end{align}

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?

\begin{align} \\ & Final \: price \\ & = original \: price \times \:\left(\frac{ 100 + a}{100}\right) \times \:\left(\frac{ 100 + b}{100}\right) \\ & = 25 \times \:\left(\frac{ 100 + 20}{100}\right) \times \:\left(\frac{ 100 + 40}{100}\right) \\ & = 42 Rs. \end{align}

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}

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