The percentage increase in the total number of students of a school over that in the previous year.
$Y e a r$ $P e r c e n t a g e i n c r e a s e$
$1999 - 2000$ $20 %$
$2000 - 2001$ $30 %$
$2001 - 2002$ $10 %$
Find the effective percentage increase in the number of students from $1998 - 1999$ to $2000 - 2001$ .

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Solution

Let the total number of students of the school in the year $1998 - 1999$ be $x$ .
$∴$ Number of students in the year $1999 - 2000 = x + 20$ % of $x = x + \frac{20}{100} \times x = x + \frac{x}{5} = \frac{6 x}{5}$
Similarly no. of students in the year $2000 - 2001 = \frac{6 x}{5} + 30$ % of $\frac{6 x}{5} = \frac{6 x}{5} + \frac{30}{100} \times \frac{6 x}{5} = \frac{78 x}{50}$
$∴$ Effective increase in number of students $= \frac{78 x}{50} - x = \frac{28 x}{50}$
Thus, effective percentage increase $= \frac{I n c r e a s e i n n u m b e r o f s t u d e n t s}{O r i g i n a l n u m b e r o f s t u d e n t s} \times 100 = \frac{\frac{28 x}{50}}{x} \times 100 = 56$ %

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