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?

The correct answer is 20.

Logic and Pattern Analysis:

Let us analyze the relationship between the numbers given in the problem statement.

First Pair (15 is related to 45):

Divide the square of the first number by 5 to obtain the second number:

$\frac{{15}^2}{5}=\frac{225}{5}=45$

Alternatively, multiply the first number by one-fifth of itself:

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

Second Pair (25 is related to 125):

Applying the exact same logic to the second pair:

$\frac{{25}^2}{5}=\frac{625}{5}=125$

Alternatively:

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

Finding the Unknown Number related to 80:

Let the required number be $x$.

Following the established pattern, $x$ must satisfy:

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

Multiply both sides by 5:

$x^2=80\times 5$

$x^2=400$

Taking the square root of both sides:

$x=\sqrt{400}=20$

Therefore, the number related to 80 using the same logic is 20.