15 is related to 45 following a certain logic. Following the same logic, 25 is related to 125. Which of the following numbers is related to 80 using the same logic?

Let's establish the underlying relationship pattern between the pairs:
*First Pair ($15\to 45$):**

$$15\times \left(\frac{15}{5}\right)=15\times 3=45$$

Alternatively written as: $\frac{15^2}{5}=\frac{225}{5}=45$
*Second Pair ($25\to 125$):**

$$25\times \left(\frac{25}{5}\right)=25\times 5=125$$

Alternatively written as: $\frac{25^2}{5}=\frac{625}{5}=125$

The common logic is:

$$\text{Second Number}=\frac{(\text{First Number}{)}^2}{5}$$

Let the unknown number be $x$. Applying the same logic:

$$\frac{x^2}{5}=80$$

$$x^2=80\times 5$$

$$x^2=400$$

$$x=\sqrt{400}=20$$

Hence, the required number is 20.