Question

(i) A number when increased by 23% becomes 861; find the number. (ii) A number when decreased by 16% becomes 798; find the number.

Answer 1

(i) Let the number be x
By the given condition,
$x+\frac{x\times 23}{100}=861\Rightarrow \frac{100x+23x}{100}=861$
$\Rightarrow x\left(\frac{123}{100}\right)=861\Rightarrow x=\frac{861\times 100}{123}=7\times 100$
= 700
$\therefore$ the required number = 100
(ii) Let the number = 100
By the given condition,
$x-\frac{x\times 16}{100}=798\Rightarrow \frac{100x-16x}{100}=798$
$\Rightarrow \frac{84}{100}x=798$
$\Rightarrow x=\frac{798\times 100}{84}=\frac{114\times 100}{12}$ = $\frac{114\times 25}{3}$
= 38 $\times$ 25 = 950
$\therefore$ The required number = 950