Correct option is D
Solution:
When two digits a and b are given, we can form two 2-digit numbers:
First number: ab → means 10 × a + b
Second number: ba → means 10 × b + a
Now, add both numbers:
(10a + b) + (10b + a)
= 11a + 11b
= 11 × (a + b)
So, the sum of both numbers is 11 times the sum of the digits.
We are told this total is a perfect square.
So now we need to find when 11 × (a + b) is a perfect square.
Let's check the smallest perfect square divisible by 11:
121 is a perfect square (11 × 11)
That means:
11 × (a + b) = 121
→ a + b = 11
Final Answer: (d) 11
