Question

A natural number, when decreased by 13, equals 140 times its reciprocal. Find the number.

• A. x = 20
• B. x = 90
• C. x = 60
• D. x = 10

Answer 1

The correct option is A

x = 20

Let the natural number be x.
According to the question.
$x-13=\frac{140}{x}$
On multiplying by x on both sides, we get
$\Rightarrow x^2-13x-140=0x^2+(7x-20x)-140=0\Rightarrow x^2+7x-20x-140=0\Rightarrow x(x+7)-20(x+7)=0\Rightarrow (x+7)(x-20)=0$
Now, x + 7 = 0$\Rightarrow$ x = -7 which is not possible because natural number is always greater than zero and $x-20=0\Rightarrow x=20$.
Hence, the required natural number is 20.