In the following numbers-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 numbers on the left side of :: is the same as that of the right side of :: ?

(NOTE: Operations should be performed on the whole numbers without breaking down the numbers into its constituent digit.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 : 529 :: 21 : Y

Correct option is D

Given: 

X : 529 :: 21 : Y

Logic: 

Square of  (1st + 5) = 2nd letter.

After analyze the options - 

(d) X = 18 , Y = 676

​$$(18 + 5)^2 = 23^2 = 529 \\ \ \\ (21 + 5)^2 = 26^2 = 676$$​​

This is the follows. 

Correct answer is (d).