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.)

(16, 7, 112)

(8, 12, 96)

To find the set that follows the same logic as the given sets, let us analyze the relationship between the numbers in each of the provided sets:
1. First set: $(16,7,112)$
2. Second set: $(8,12,96)$

Let the numbers in each set be represented as $(A,B,C)$.
Let us examine the mathematical operation that relates the first two numbers $A$ and $B$ to the third number $C$.

For the first set:
$A=16$, $B=7$, $C=112$
Multiplying $A$ and $B$:
$16\times 7=112$
Thus, the relationship is:
$A\times B=C$

Let us verify this relationship with the second set:
$A=8$, $B=12$, $C=96$
Multiplying $A$ and $B$:
$8\times 12=96$
The pattern holds true: the third number is the product of the first two numbers.

Now, let us test the given options to see which set satisfies this logic:

Option 1: $(13,7,96)$
Product of first two numbers: $13\times 7=91$ (not equal to 96)

Option 2: $(14,9,128)$
Product of first two numbers: $14\times 9=126$ (not equal to 128)

Option 3: $(12,5,65)$
Product of first two numbers: $12\times 5=60$ (not equal to 65)

Option 4: $(15,8,120)$
Product of first two numbers: $15\times 8=120$ (equal to 120)

Only the set $(15,8,120)$ satisfies the relationship $A\times B=C$.
Therefore, the correct option is $(15,8,120)$.