Percentage

Percentage

The term percentage means 'for every hundred'.

It can be defined as follows

"A percentage is a fraction whose denominator is 100 and the numerator of the fraction is called the rate percentage." Percentage is denoted by the sign'%'.

If we have to find y % of x

then      y % of \[x=x\times \frac{y}{100}\]

·         Percentage-Decimal Conversion

e.g., 125% = 1.25

35 % = 0.35

2% = 0.02

·         Percentage-Fraction Conversion

e.g., \[\frac{2}{5}=0.4\times 100%=40%\]

\[\frac{20}{400}=\frac{4}{\frac{400}{4}}=\frac{5}{100}=5%\]

More About Percentage

·         y% of x = x% of y

·         y% of \[x=x\times \frac{y}{100}\]

·         To find how much percentage one quantity is of another. Required percentage

\[\text{=}\frac{\text{The quantity to be expressed in percentage}}{\text{2nd quantity (in respect of which the percentage hasto be obtained)}}\text{ }\!\!\times\!\!\text{ 100}\]

Quicker One

Ø  Percentage increase \[=\frac{\text{Increase}}{\text{Original}\,\,\text{value}}\times 100\]

Ø  Percentage decrease \[=\frac{\text{Decrease}}{\text{Original}\,\,\text{value}}\times 100\]

Ø  When a value/number/quantity A is increased or decreased by b% then new value/number/quantity will be \[=\frac{100\pm b}{100}\times A\]

Ø  If a is x% more than b, then be is less than a by

\[\left[ \frac{x}{100+x}\times 100 \right]%\]

Ø  When the value of an object is first changed (increased or decreased) by x% and then changed by y%, then net effect is given as \[=\left[ \pm \,\,x\,\,\pm \,\,y+\frac{(\pm x)(\pm y)}{100} \right]%\]

(\[+\] ve sign indicates increase, \[-\] ve sign indicates decrease.)

Ø  If the price of a commodity increases or decreases by a%, then the decrease or increase in consumption so as not to increase or decrease the expenditure is equal to \[\left( \frac{a}{100\pm a} \right)\times 100%\]