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

Given:

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

 To do:

We have to find the number.

Solution:

Let the required natural number be $x$.

Reciprocal of $x$ is $\frac{1}{x}$.

According to the question,

$x+12=160(\frac{1}{x})$

$x(x+12)=160$

$x^2+12x-160=0$

Solving for $x$ by factorization method, we get,

$x^2+20x-8x-160=0$

$x(x+20)-8(x+20)=0$

$(x+20)(x-8)=0$

$x+20=0$ or $x-8=0$

$x=-20$ or $x=8$

$-20$ is not a natural number. Therefore, the value of $x$ is $8$.

The required natural number is $8$. 

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Updated on: 10-Oct-2022

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