Number S is obtained by squaring the sum of digits of a two-digit number D. If difference between S and D is 27, then the two digit number D is ............

Let us solve this problem by using the options, 
Option A: 24, sum is 6. The square of the sum of the digits is 36, the difference between S and D will be 12. 
Option B: 54, the sum is 9. The square of the sum of the digits is 81, the difference between S and D will be 27. 
Option C: 34, the sum is 7. The square of the sum of the digits is 49, the difference is between S, and D will be 15. 
Option D: 45, sum is 9, Square of the sum of the digits is 81, difference between S and D will be 36. 

Hence, Option B is the answer.