**Problem Analysis**

Let's assume the natural number as "x". According to the problem statement, when this number is increased by 12, it equals 160 times its reciprocal. Mathematically, we can represent this as:

x + 12 = 160 * (1/x)

To find the value of "x", we need to solve this equation.

**Solving the Equation**

We can start by simplifying the equation:

x + 12 = 160/x

Multiplying both sides of the equation by "x" to eliminate the denominator:

x(x + 12) = 160

Expanding the left side of the equation:

x^2 + 12x = 160

Rearranging the equation to obtain a quadratic form:

x^2 + 12x - 160 = 0

**Factoring the Quadratic Equation**

To solve the quadratic equation, we can factor it. Let's find two numbers whose product is -160 and whose sum is 12. After factoring, we get:

(x + 20)(x - 8) = 0

Setting each factor equal to zero and solving for "x":

x + 20 = 0 or x - 8 = 0

x = -20 or x = 8

**Finding the Valid Solution**

Since we are dealing with a natural number, we can discard the negative solution (-20) as it is not a valid solution. Therefore, the only valid solution is x = 8.

Hence, the natural number is 8.

Let the natural number be 'x'.
The number increased by 12=x+12.
The reciprocal of the number=1/x.
Equation is,
x+12=160×1/x.
x+12=160/x
x(x+12)=160
x^2+12x=160
x^2+12x-160=0
x^2+20x-8x-160=0
x(x+20)-8(x+20)=0
(x-8) (x+20)
x-8=0 x+20=0
x=8. x=-20.
Since 'x' is a natural number,
The required number=x=8.