In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. 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 their constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting /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.)

36, 289
58, 465

The correct option is 23, 185.

To understand why this is the correct set, we need to analyze the mathematical relationship between the first number and the second number in the given examples.

Let the first number in each pair be represented as x and the second number as y. By analyzing the given pairs, we can establish the following pattern:

$$y=(x\times 8)+1$$

Let us verify this logic with the given pairs:

1) For the first pair (36, 289):

Here, the first number is:

$x=36$

Applying the logic, we multiply by 8 and add 1:

$$(36\times 8)+1=288+1=289$$

This matches the second number 289.

2) For the second pair (58, 465):

Here, the first number is:

$x=58$

Applying the logic, we multiply by 8 and add 1:

$$(58\times 8)+1=464+1=465$$

This matches the second number 465.

Now, let us test the correct option (23, 185) using the same rule:

Here, the first number is:

$x=23$

Applying the logic, we multiply by 8 and add 1:

$$(23\times 8)+1=184+1=185$$

This matches the second number 185, confirming that this pair follows the exact same mathematical pattern.