Question

A natural number, when increased by 8, equals 240 times its reciprocal. Find the given number.

Answer 1

Step 1: Construct the equation based on given condition.

Let the required natural number be $x$.
According to the question,
$x+8=\frac{240}{x}$
Multiplying both sides by $x$, we get,
$x^2+8x-240=0,$

Step 2: Find roots using factorization.

By splitting the middle term, we get,
$\Rightarrow x^2+(20x-12x)-240=0$
$\Rightarrow x^2+20x-12x-240=0$
$\Rightarrow x(x+20)-12(x+20)=0$
$\Rightarrow (x+20)(x-12)=0$
$\Rightarrow x=12,-20$
Since, $x$ is a natural number, therefore $x\ne -20$.
$\Rightarrow x=12$

Hence, the required natural number is $12$.