x and y are 2 different digits. If the . . .

Question : x and y are two different digits. If the sum of the two digit numbers formed by using the digits is a perfect square, then the value of x+y is 

a) 10

b) 11

c) 12

d) 13

Doubt by Pushkar

Solution : 

Let us assume that the digit at the unit place is x and the digit at the ten's place be y. 

So 

Original number = 10y+x

Reverse number = 10x+y

ATQ 

Perfect Square =
Original number + Reverse number

Perfect Square =10y+x + 10x+y
Perfect Square = 11x+11y
Perfect Square = 11(x+y)

Clearly Least value of x+y to be a perfect square is 11.

Hence, b) would be the correct option.