20 is related to 30 following a certain logic. Following the same logic, 30 is related to 45. Which of the following numbers is related to 120 using the same logic?

The correct answer is 80.

Let's analyze the logic relating the numbers step-by-step:

First, we look at the relationship between the first pair of numbers, 20 and 30:
If we divide the second number by the first number, we get:

$\frac{30}{20}=1.5$

This means 20 is multiplied by 1.5 to get 30.

Next, let's verify if the same logic applies to the second pair, 30 and 45:

$\frac{45}{30}=1.5$

This confirms that the logic is to multiply the first number by 1.5 (or $\frac{3}{2}$) to get the second related number.

Now, let $x$ be the number that is related to 120 using this same logic. This means:

$x\times 1.5=120$

We can solve for $x$ by dividing 120 by 1.5:

$x=\frac{120}{1.5}$

$x=\frac{120}{\frac{3}{2}}$

$x=120\times \frac{2}{3}$

$x=40\times 2$

$x=80$

Therefore, the number related to 120 using the same logic is 80.