- The sum of the digits of a two-digit number is 12. The new number formed by reversing  the digits is greater than the original number by 54.★To find:- The original number.★Solution:- Let x & y are the two digits of the number.We need to know, Any two digit number WHOSE first digit is 'x' & second digit is 'y' is written in the form 10x+y.We have,The original number = 10x+yNumber formed by reversing digits = 10y+xGiven that the sum of the digits of a two-digit number is 12.Therefore, ➺ x + y = 12 ----(1)Also,the new number formed by reversing  the digits is greater than the original number by 54.Therefore, ➺ 10y+x = (10x+y) + 54 ➺ 10y+x - (10x+y) = 54➺ 10y+x-10x-y = 54 ➺ 9Y - 9x = 54➺ 9(y-x) = 54 ➺ y - x = 54/9 ➺ y - x = 6 -----(2)Adding equation (1)&(2),x + y = 12-x+ y  = 6     2y = 18 ➺y = 18/2 ➺y = 9 Substituting VALUE of 'y' in equation (1), ➺ x + y = 12 ➺ x + 9 = 12 ➺ x = 12 - 9 ➺ x = 3 Original number:- ➺ 10x + y ➺ 10(3) + 9 ➺ 30 + 9 ➺ 39 Hence,the original number is 39._____________★Verification★Given sum of the digits of a two-digit number is 12.PUTTING values, ➜x + y = 12 ➜3 + 9 = 12 ➜12 = 12 Given,the new number formed by reversing  the digits is greater than the original number by 54.No formed by reversing digits = 93 Putting values,➜ 93 - 39 = 54 ➜ 54 = 54 Hence verified! _____________