Percentages Formulas

Percent means for every hundred.  $x\% = \displaystyle\frac{x}{{100}}$
Percentage conversions: *
$1 = 100\%$;

$\displaystyle\frac{1}{2}$ = 50% ;

$\displaystyle\frac{1}{3}$ = 3313% or 33.33;

$\displaystyle\frac{1}{4}$ = 25% ;$\displaystyle\frac{3}{4}$ = 75% ;

$\displaystyle\frac{1}{5}$ = 20%;

$\displaystyle\frac{1}{6}$ = 1623% or 16.66%;

$\displaystyle\frac{1}{7}$ = 1427% or 14.28%;

$\displaystyle\frac{1}{8}$ = 1212% or 12.5%;

$\displaystyle\frac{1}{9}$ = 1119% or 11.11% ;

$\displaystyle\frac{1}{{10}}$ = 10%;

$\displaystyle\frac{1}{{11}}$ = 9111%  or  9.09%;

$\displaystyle\frac{1}{{12}}$ = 813%;

Formula 1:

A is what percentage of B?
$\Rightarrow \displaystyle\frac{{\rm{A}}}{{\rm{B}}}{\rm{ \times 100}}$

Formula 2:

A is howmuch percent greater than B?
$\Rightarrow \displaystyle\frac{{{\rm{A - B}}}}{{\rm{B}}}{\rm{ \times 100}}$

Formula 3:

A is howmuch percent less than B?
$\Rightarrow \displaystyle\frac{{{\rm{B - A}}}}{{\rm{B}}}{\rm{ \times 100}}$

Formula 4:

If A is increased by K% then the new number is $(100 + K)\% \times A$
But there are several methods available to calculate easily.

Example: A is increased by 20% then the new number can be calculated as

Method 1: $(100 + 20)\% \times A \Rightarrow 120\% \times A$
Method 2: Calculate 20% of the given number and add to the original number A. $\Rightarrow A + (20\% \times A)$
Method 3: If basic ratio is available for the given percentage then $\Rightarrow A + (\displaystyle\frac{1}{5} \times A) \Rightarrow \frac{6}{5} \times A$

Formula 5:
If A is decreased by K% then the new number is $(100 - K)\% \times A$
But there are several methods available to calculate easily.

Example: A is decreased by 20% then the new number can be calculated as

Method 1: $(100 - 20)\% \times A \Rightarrow 80\% \times A$
Method 2: Calculate 20% of the given number and substract from the original number A. $\Rightarrow A - (20\% \times A)$
Method 3: If basic ratio is available for the given percentage then $\Rightarrow A - (\displaystyle\frac{1}{5} \times A) \Rightarrow \frac{4}{5} \times A$

Formula 6:

$A\% (B) = B\% (A)$

Formula 7:

If several percentages are acting on the same number then we can add all the percentages.
${x_1}\% (K) + {x_2}\% (K) + {x_3}\% (K)... = ({x_1} + {x_2} + {x_{3...}})\% (K)$

Formula 8:

If a number K got increased by A% and B% successively then the final percentage is given by $\left( {A + B + \displaystyle\frac{{AB}}{{100}}} \right)\%$
Note1: If decreased then substitute +A% with -A%

Note2: Any two dimensional diagram like square, rectangle, rhombus, triangle, circle, parrellogram, sides got increased or decreased by certain percentages, then the percentage change in the area can be calculated by the above formula