# Percentage Formulas, Shortcuts, Tips and Tricks

## Important Notes on Percentage

• Percentage increase = $\frac{Actual\, increase}{original \,quantity} \times 10$
• Percentage decrease = $\frac{Actual\, decrease}{original\, quantity} \times 100$
• Change in value = $\left ( \frac{Percentage \,change}{100} \right )\times Initial\, value$
• If percentage increase is p percentage then new value = $\left ( 1+\frac{p}{100} \right )\times initial\, value$
• If the value of an item goes up/down by x%, the percentage reduction/increment to be now made to bring it back to the original level is $\frac{100x}{(100\pm x)}$ %
• If A is x % $\frac{more}{less}$ than B, Then B is $\frac{100x}{(100\pm x)}\%\frac{less}{more}$ than A.
• If the price of an item goes up/down by x % then the quantity consumed should be $\frac{reduced}{increased}\, by\, \frac{100}{(100\pm x)}$ % so that the total expenditure remains the same.
• If $p_{1},p_{2},p_{3}$ …………. are successive percentages of change then. Final Value = $((1\pm p_{1}\%)(1\pm p_{2}\%)(1\pm p_{3}\%).............)\times \,initial\, value$
• If a certain is first increased by x% and then increased by another y%, then the effective percentage increase in the quantity will be $\left ( x+y-\frac{xy}{100} \right )$ %.

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