Question

school strength increase by 20% in one year and decrease by 20% in next year.is the final strength greater or less than the orivinal one and by how much

Answer 1

let original strength be 100
20%increased =(20/100×100)+100
=120
20%decreased =120-(20/100×120)
= 120-24=96
so , the final strength will less than original

Answer 2

$let \: the \: strength \: of \: the \: school = x \\ then \: increase \: in \: 20\% = x + 20\% \\ = > \: \: x + \frac{20}{100} \times x \\ = > \: \: x (1 + \frac{20}{100} ) \\ = > \: \: x( \frac{120}{100} ) \\ = > \: \: x( \frac{6}{5} ) \\ = > \: \: \frac{6x}{5}$
$again \: when \: 20\%decreases \\ = > \: \: \frac{6x}{5} - 20\% \\ = > \: \: \frac{6x}{5} - \frac{20}{100}x \\ = > \: \: \frac{6x}{5} - \frac{x}{5} \\ = > \frac{5x}{5} \\ = > \: \: x$
Therefore the final strength is similar to that of the original one.