Question

A natural number, when increased by $12$, equals $160$ times its reciprocal. Find the number.

Answer 1

Let the natural number be $x$
Therefore according to question the following equation can be formed:
$x+12=\frac{160}{x}$
$\Rightarrow x^2+12x=160$.
$\Rightarrow x^2+12x-160=0$
$\Rightarrow x^2+20x-8x-160=0$
$\Rightarrow x(x+20)-8(x+20)=0$
$\Rightarrow (x+20)(x-8)=0$
$\therefore (x+20)=0or(x-8)=0$
$x=-20orx=8$
As $x=-20$ is not a natural number therefore value of $x$ is $8$
So, $x=8$