Quant · Arithmetic

Percentages

3 sub-topics · 21 lessons · 61 questions · 10 PYQs

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Percentage Basics7 lessons · 20 questions · 2 PYQs

Percentage Change7 lessons · 21 questions · 4 PYQs

Percentage Applications7 lessons · 20 questions · 4 PYQs

Formula sheet

Population after changing yearly rates
$P_n=P_0\prod\left(1+\frac{r_i}{100}\right)$
Multiplying factor
$\text{new}=\text{old}\times\left(1\pm\frac{r}{100}\right)$
x% of y equals y% of x
$x\%\text{ of }y=\frac{xy}{100}=y\%\text{ of }x$
Up and down by the same percentage
$+x\%\text{ then }-x\%:\ \text{net}=-\frac{x^2}{100}\%$
Fraction–percentage equivalents to memorise
$\frac1{6}=16\tfrac23\%,\ \frac17=14\tfrac27\%,\ \frac18=12\tfrac12\%,\ \frac19=11\tfrac19\%,\ \frac1{11}=9\tfrac1{11}\%$
More than versus less than
$A=\left(1+\frac{r}{100}\right)B\Rightarrow B\text{ is }\frac{100r}{100+r}\%\text{ less than }A$
One quantity as a percentage of another
$\frac{A}{B}\times100\%=\text{A as a percentage of B}$
Net of two successive changes
$a\%\text{ then }b\%:\ \text{net}=a+b+\frac{ab}{100}\ (\text{use }-b\text{ for a fall})$