Percentage Questions Answers Formulas, Tips and Tricks

• 1. Concept of percentage or Percentage formula

  
  

  By a certain percent, we mean that many hundredths.
  
  Thus, x percent means x hundredths, written as x%.
  
  To express x% as a fraction: We have, x%
  
  \begin{aligned} \frac{x}{100} \\
  Thus, & 10\% = \frac{10}{100} = \frac{1}{10} \\
  30\% = \frac{30}{100} = \frac{3}{10} \\
  \end{aligned}
  
  In simple terms we can conclude that percentage symbol "%" means 1/100
  
  In case we are having a fraction and we have to calculate its percentage then we will multiply it by 100.
  that is,
  \begin{aligned}
  \frac{a}{b} = \left(\frac{a}{b}\times100\right)\%
  \end{aligned}
  
  So if we get a question like 1 is what percent of 4, then we will solve it as,
  
  \begin{aligned}
  \frac{1}{4}*100 = 25\% \\
  Similarly & \frac{3}{5}*100 = 60\% \\
  \end{aligned}

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• 2. Increase or decrease in percentage with price

  
  

  If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure will be,
  
  \begin{aligned}
  \left[ \frac{R}{(100+R)}\times 100 \right]\%
  \end{aligned}
  
  If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure will be
  
  \begin{aligned}
  \left[ \frac{R}{(100-R)}\times 100 \right]\%
  \end{aligned}

  • Comment on this formula

• 3. Results on population

  
  

  Formula's on result of population are very important when we have to calculate the population n years after or n years before,
  
  Let the population of a town be P now and suppose it increases at the rate of R% per annum, then
  \begin{aligned}
  1. & \text{Population after n years =}P\left(1+\frac{R}{100}\right)^n \\
  
  2.& \text{Population before n years =} \frac{P}{\left(1+\frac{R}{100}\right)^n} \\
  \end{aligned}

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• 4. Results on Depreciation

  
  

  We know that value of a machine depreciate with time, so it will decrease with the time. To calculate the value of machine after n years or before n years, we use these formula's
  
  Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum.
  
  
  \begin{aligned}
  1. & \text{Population after n years =}P\left(1-\frac{R}{100}\right)^n \\
  
  2.& \text{Population before n years =} \frac{P}{\left(1-\frac{R}{100}\right)^n} \\
  \end{aligned}

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• 5. Important results for Percentage

  
  

  The formulas we are going to mention below is same as of increase or decrease in consumption with increase or decrease in the commodity price, just here we are in a bit different context.
  
  If A is R% more than B, then B is less than A by
  
  \begin{aligned}
  \left[ \frac{R}{(100+R)}\times 100 \right]\%
  \end{aligned}
  
  If A is R% less than B, then B is more than A by
  
  \begin{aligned}
  \left[ \frac{R}{(100-R)}\times 100 \right]\%
  \end{aligned}

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Percentage Questions Answers