Select the set in which the numbers are related in the same way as are the numbers of the given 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, 4, 20)

(28, 7, 35)

The correct option is (52, 13, 65).

To find the matching set, let us analyze the mathematical relationship between the numbers in the given sets of the form:

$(A,B,C)$

First given set: (16, 4, 20)

If we add the first and second numbers, we get the third number:

$16+4=20$

Additionally, we can observe the relationship based on the middle number (B):

$A=4\times B\Rightarrow 16=4\times 4$

$C=5\times B\Rightarrow 20=4\times 5$

Second given set: (28, 7, 35)

Applying the same logic:

$28+7=35$

Using the middle number (B = 7):

$A=4\times B\Rightarrow 28=4\times 7$

$C=5\times B\Rightarrow 35=5\times 7$

Thus, the logic followed in both given sets is that the numbers are in the ratio 4 : 1 : 5, where:

$A+B=C$

Now, let us test this relationship on the option (52, 13, 65):

Checking the sum:

$52+13=65$

Checking the ratios with the middle number (B = 13):

$52=4\times 13$

$65=5\times 13$

Since the set (52, 13, 65) satisfies the logic perfectly, it is the correct answer.