In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which number should replace X and Y so that the pattern followed by the two number on the left side of :: is the 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 : 346 :: 9 : Y

Given: X : 346 :: 9 : Y

Logic:  Cube of 1st number = 2nd number+3 

After analyze the options- 

From option (c): X = 7 , Y = 732

​$$7^3 + 3= 343+3 = 346\\ \ \\9^3 +3 = 729 +3= 732$$

So, X = 7 , Y = 732 is followed the logic.

Thus, correct option is (c).