Question

State true or false. A natural number, when increased by 12, equals 160 times its reciprocal. Such a number is 8.

• A. True
• B. False

Answer 1

The correct option is A

True

Let the natural number be x.
According to the question.
$x+12=\frac{160}{x}$
On multiplying by x on both sides, we get
$\Rightarrow x^2+12x-160=0x^2+(20x-8x)-160=0\Rightarrow x^2+20x-8x-160=0\Rightarrow x(x+20)-8(x+20)=0\Rightarrow (x+20)(x-8)=0$
Now, x + 20 = 0$\Rightarrow$ x = -20 which is not possible because natural number is always greater than zero and $x-8=0\Rightarrow x=8$.
Hence, the required natural number is 8.