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/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.)

(3, 12, 26)

(7, 9, 53)

The correct option is (7, 5, 25).

Logic/Pattern:

In each set of three numbers (A, B, C), the third number is obtained by subtracting 10 from the product of the first two numbers.

$C=(A\times B)-10$

Let's verify this pattern with the given sets:

1. First set: (3, 12, 26)

$(3\times 12)-10=36-10=26$

2. Second set: (7, 9, 53)

$(7\times 9)-10=63-10=53$

Now, let's test the given options to find which one follows the exact same pattern:

Option 1: (4, 9, 16)
$(4\times 9)-10=36-10=26\ne 16$
(Incorrect)

Option 2: (12, 4, 114)
$(12\times 4)-10=48-10=38\ne 114$
(Incorrect)

Option 3: (7, 5, 25)
$(7\times 5)-10=35-10=25$
(Correct)

Option 4: (5, 15, 45)
$(5\times 15)-10=75-10=65\ne 45$
(Incorrect)

Hence, (7, 5, 25) is the set that follows the same relationship.