In the following number pairs, the second number is obtained by performing certain mathematical operations on the first number. Now what numbers should come in place of X and Y so that the pattern followed by the numbers written outside :: is the same as the numbers written to the right of ::. (Note: Mathematical operations should be performed without separating the factors of whole numbers. For example, 13 – mathematical operations like addition/subtraction/multiplication etc. can be performed on the number 13. Separating the factors of 13, 1 and 3, and performing mathematical operations on 1 and 3 are not allowed.)
X : 47 :: 16 : Y

X : 47 :: 16 : Y

Logic: 1st number $$\times$$ 7 = new number, new number - 2 = 2nd number.

Lets check by options;

7 : 47 :: 16 : 110

1st pair:

7 $$\times$$ 7 = 49, 49 - 2 = 47

2nd pair:

16 $$\times$$ 7 = 112, 112 - 2 = 110 (Follow)

8 : 47 :: 16 : 110

1st pair:

8 × 7 = 56, 56 - 9 = 47

2nd pair:

16 $$\times$$ 7 = 112, 112 - 2 = 110 (Does not follow)

7 : 47 :: 16 : 111

1st pair:

7 × 7 = 49, 49 - 2 = 47

2nd pair:

16 $$\times$$​ 7 = 112, 112 - 1 = 111 (Does not follow)​

8 : 47 :: 16 : 111

1st pair:

8 × 7 = 56, 56 - 9 = 47

2nd pair:

16 $$\times$$​ 7 = 112, 112 - 1 = 111 (Does not follow)​

Thus, the correct answer is (a).