Question

A number is increased by a$\%$ and then b$\%$. By what p.c. the original number is changed?

Answer 1

Let the no' be N

i) $\uparrow$ by $a\%$

$\Rightarrow N+\frac{a}{100}N=\left(\frac{100+a}{100}\right)N$

ii) $\uparrow$ by $b\%$

$\Rightarrow \left(\frac{100+a}{100}\right)N+\frac{b}{100}\left(\frac{100+a}{100}\right)N$

$\Rightarrow \left(\frac{100+a}{100}\right)\left(\frac{100+b}{100}\right)N$

$\Rightarrow (1+\frac{a}{100}+\frac{b}{100}+\frac{ab}{10000})N$

$\Rightarrow \uparrow by(a+b+\frac{ab}{100})\%$