Question:
A natural number, when increased by 12, becomes equal to 160 times its reciprocal. Find the number.
Solution:
It is given that a number when increased by 12 becomes 160 times its reciprocal.
We have to find the number.
Let the number beĀ x
Reciprocal of $x=\frac{1}{x}$
According to the question
$x+12=160 \times \frac{1}{x}$
$x^{2}+12 x=160$
$x^{2}+12 x-160=0$
$x^{2}+20 x-8 x-160=0$
$x(x+20)-8(x+20)=0$
$(x+20)(x-8)=0$
$x=-20,8$
since $-20+8 \neq \frac{160}{-20}$
Therefore $x=8$
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