Question

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

Answer 1

Step 1: Construct the equation based on given condition.
let the required natural number be $x$.
According to the question,
$x+12=\frac{160}{x}$
On multiplying by $x$ on both sides, we get
$x^2+12x-160=0,$

Step 2: Find roots using factorization.
By splitting the middle term, we get :
$\Rightarrow x^2+(20x-8x)-160=0$
$\Rightarrow x^2+20x-8x-160=0$
$\Rightarrow x(x+20)-8(x+20)=0$
$\Rightarrow (x+20)(x-8)=0$
$\Rightarrow x=8$
$[x\ne -20\text{because it is not a natural number}]$
hence, the required natural number is $8$.