217 is related to 115 following a certain logic. Following the same logic, 183 is related to 81. To which of the given options is 234 related, following the same logic? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying 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 option is 132.

Let us analyze the relationship between the pairs of numbers given in the question.

First Pair: (217, 115)

If we subtract 115 from 217, we get:

$217-115=102$

Alternatively, the second number is obtained by:

$(217+13)÷2=230÷2=115$

Or simply dividing by 2 and adding 6.5:

$217-102=115$

Let us check the rule: (First number - 13) ÷ 2 = Second number

For 217:

$(217-13)÷2=204÷2=102$ (Not 115)

Let's check another simple rule: (First number ÷ 2) + 6.5 = Second number

$217÷2=108.5$

$108.5+6.5=115$

Let us test this logic on the Second Pair: (183, 81)

$183÷2=91.5$

$91.5-10.5=81$

Let's find a unified pattern using subtraction:

Difference in pair 1: $217-115=102$

Difference in pair 2: $183-81=102$

The logic is simple: The second number is obtained by subtracting 102 from the first number.

Applying the same logic to 234:

$234-102=132$

Therefore, 234 is related to 132.