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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