In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is
same as that on the right side of ::?
(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.)

X:112::15:Y

X:112::15:Y

Logic: 1st × (1st letter - 3) + 4 = 2nd letter. 

From the given options - 

(b) X=12,Y=184

12 × (12 - 3) + 12 × 9 + 4 = 108 + 4 = 112

15 × (15 - 3) + 15 × 12 + 4 = 180 + 4 = 184

Correct answer is (b).