# Quantitative - Percentage

## Percentage Description

• By percent, we mean that many hundredths.
• Thus x percent means x/100, written as x%.
• A fraction whose denominator is 100 is called a percentage and the numerator of the fraction is called rate per cent.
• A student gets 60% marks in arithmetic means that he obtained 60 marks out of 100. So if full marks are 500 he gets  ${\frac{60}{100}\times 500}$ = 300 marks.

Important Formulas

1. If A is R% more than B, then B is less than A by ${[\frac{R}{100+R}\times 100]}$%

2. If A is R% less than B, than B is more than A by ${[\frac{R}{100-R}\times 100]}$%

3. Result on Population.
Let P be the population of a town now. Let it increase at R% per annum.
(i) Population after n years = ${P(1+\frac{R}{100})^{n}}$
(ii) Population n years ago = ${ \frac{P}{(1+\frac{R}{100})^{n}}}$

4. Result on Depreciation.
Let the present value of a machine is Rs. P. Let it depreciate at R% per annum. Then
(i) Value of Machine after n years = ${P(1-\frac{R}{100})^{n}}$
(ii) Value of Machine n years ago =  ${ \frac{P}{(1-\frac{R}{100})^{n}}}$
5. If the price of a commodity increases by R% then reduction in consumption so as not to increase the expenditure is                    Reduction % = ${[\frac{R}{100+R}\times 100]}$%

6.
If the price of the commodity decrease by R%, then increase in consumption, so as not to decrease the expenditure is
Increase % in consumption = ${[\frac{R}{100-R}\times 100]}$%

7. If the value of a number first increases by x% and later decreased by x% then net change is always decrease which is ${\frac{x^{2}}{100}}$ %

8. If a value first increased by x% and then decreased by y% than there is ${(x-y-\frac{xy}{100})}$ % increase or decrease according to the +ve or -ve sign respectively.

9. If the value is increased successively by x% and y% then the final increase is given by ${(x+y-\frac{xy}{100})}$%

10. If the sides of a triangle, rectangle, square, rhombus or any 2-dimensional figure increases by x% then area is increased by  ${(2x+\frac{x^{2}}{100})}$%
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