Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
(108, 27, 9)
(132, 33, 11)

The correct option is (180, 45, 15).

To determine the correct set, let us analyze the mathematical relationship between the numbers in the given sets: (108, 27, 9) and (132, 33, 11).

Let each set be represented in the format (A, B, C).

First Set: (108, 27, 9)

Notice the relationship between the third number (C) and the second number (B):

$9\times 3=27$

Now, notice the relationship between the second number (B) and the first number (A):

$27\times 4=108$

Alternatively, looking at the third number (C) and the first number (A):

$9\times 12=108$ (since $3\times 4=12$).

Second Set: (132, 33, 11)

Applying the same pattern:

Relationship between C and B:

$11\times 3=33$

Relationship between B and A:

$33\times 4=132$

Alternatively, looking at C and A:

$11\times 12=132$.

Thus, the common pattern is:

$B=C\times 3$

$A=B\times 4=C\times 12$

Now, let us check the options to find the set that follows this exact pattern:

Option 1: (180, 45, 10)

$10\times 3=30\ne 45$ (Incorrect)

Option 2: (190, 45, 15)

$15\times 3=45$

$45\times 4=180\ne 190$ (Incorrect)

Option 3: (180, 45, 15)

$15\times 3=45$

$45\times 4=180$

This matches the pattern precisely!

Option 4: (180, 55, 15)

$15\times 3=45\ne 55$ (Incorrect)

Therefore, the set (180, 45, 15) follows the same pattern as the given sets.