Percentages concept:
Percentages are constantly used by us in our day to day life. Some of the situations where percentages, widely used are calculating profit and loss, rent, discount, insurance, premium and so on.
To express X% as a fraction : X% $= \frac{X}{100}$
To express $\frac{X}{Y}$ as a percent : We have, $\frac{X}{Y}$ $=\left( \frac{X}{Y} \times 100\right)$%
If the price of a commodity increases by $x%$, then the reduction in consumption so as not to increase the expenditure is $\left[\frac{X}{(100+X)}\times 100\right]$%
If the price of a commodity decreases by x%, then the increase in consumption so as not to decrease the expenditure is $\left[\frac{X}{(100-X)}\times 100\right]$%
Results on Population: Let the population of a city be P now and it increases at the rate of R% per annum, then :
Population after n years = $P\left( 1+\frac{R}{100}\right) ^{n}$
Popuation n years ago = $\frac{P}{\left(1+\frac{R}{100}\right)^{n}}$
Results on Depreciation : Let the present value of an instrument be P. Suppose it depreciates at the rate of R%. Then:
Value of the instrument after n years = $P\left( 1-\frac{R}{100}\right) ^{n}$
Value of the instrument n years ago = $\frac{P}{\left(1-\frac{R}{100}\right)^{n}}$
If X is R% more than Y, then Y is more than X by $\left[\frac{R}{(100+R)} \times 100\right]$%.
If X is R% less than Y, then Y is more than X by $\left[\frac{R}{(100-R)} \times 100\right]$%.
