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

8

Solution

Let the natural number = x

It is given that x is increased by 12, equal to 160 times its reciprocal
$x+12=\frac{160}{x}\\ x(x+12)=160\\ x^{2}+12x-160=0\\ x^{2}+20x-8x-160=0\\ x(x+20)-8(x+20)=0\\ (x+20)(x-8)=0\\ x+20=0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x-8=0\\ x=-20\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x=8$

We can’t take x = – 20 because it is given that x is a natural number.

Hence x = 8 is the required natural number.