19 is related to 209 following a certain logic. Following the same logic, 27 is related to 297. To which of the following is 61 related, following the same logic?
(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)

The correct answer is 671.

To find the correct number that is related to 61, let us first identify the underlying logic between the given pairs of numbers.

Step 1: Analyze the relationship in the first pair (19 and 209)
We can check the multiplier between 19 and 209:
$19\times 11=209$
Here, the first number is multiplied by 11 to obtain the second number.

Step 2: Verify the logic with the second pair (27 and 297)
Let us apply the same multiplication rule to the second pair:
$27\times 11=297$
Since the logic holds true for the second pair, the general pattern is to multiply the given number by 11.

Step 3: Apply the logic to 61 to find the missing number
Following the same logic, we multiply 61 by 11:
$61\times 11=671$
Therefore, 61 is related to 671.