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A natural number, when increased by $12$, equals $160$ times its reciprocal. Find the number.
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Let the natural number be $x$
ATQ, $x + 12 = \frac{160}{x}$
$x^2 + 12x = 160$
$x^2 + 12x - 160 = 0$
$(x + 20)(x - 8) = 0$
$x \neq -20, x= 8$
$\Rightarrow \text{Required natural number is } 8$
ATQ, $x + 12 = \frac{160}{x}$
$x^2 + 12x = 160$
$x^2 + 12x - 160 = 0$
$(x + 20)(x - 8) = 0$
$x \neq -20, x= 8$
$\Rightarrow \text{Required natural number is } 8$