Find the whole number which when decreased by 20 is equal to 69 times the reciprocal of the number.

Given:

A whole number which when decreased by 20 is equal to 69 times the reciprocal of the number.

 To do:

We have to find the whole number.

Solution:

Let the whole number be $x$.

According to the question,

$x-20=69(\frac{1}{x})$    (Reciprocal of $x$ is $\frac{1}{x}$)

$x-20=\frac{69}{x}$

$x(x-20)=69$

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

$x(x-20)=69$

$x^2-20x-69=0$

$x^2-23x+3x-69=0$

$x(x-23)+3(x-23)=0$

$(x-23)(x+3)=0$

$x-23=0$ or $x+3=0$

$x=23$ or $x=-3$

$-3$ is not a whole number.

Therefore, the required whole number is $23$.

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Updated on: 10-Oct-2022

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