Explanation:

The sum of such two-digit numbers could be 5 or 7 or 9 or 11 or 13 or 15. Let the first digit of the two-digit number be ‘x’ and the second digit be ‘y’.

Therefore,

he two-digit no. = (10x + y) On reversing, the two-digit number becomes = (10y + x) According to the equation we can write the equation as, (10x + y) + 27 = (10y + x)

Or, 10y – y – 10x – x = 27 Or, 9y – 9x = 27 Or, y – x = 27/9 = 3 Or, y – x = 3 (i) 

For the above equation (i) above let’s assume some value of x so that the we can calculate the value for y and obtain the final outcome we get as a two-digit number.

Case 1: x=1 ∴y – 1 = 3 or, y = 4 Therefore, two-digit no. = 14

Case 2: x=2 ∴y – 2 = 3 or, y = 5 Therefore, two-digit no. = 25 

Case 3: x=3 ∴y – 3 = 3 or, y = 6 Therefore, two-digit no. = 36

Case 4: x=4 ∴y – 4 = 3 or, y = 7 Therefore, two-digit no. = 47

Case 5: x=5 ∴y – 5 = 3 www.gradeup.co 63 or, y = 8 Therefore, two-digit no. = 58

Case 6: x=6 ∴y – 6 = 3 or, y = 9

Therefore, two-digit no. = 69 From each of the above cases, we could have the two-digits as 14 or 25 or 36 or 47 or 58 or 69. And, the sum of the digits of each of the two-digit number that we will get 14+25+36+47+58+69 = 249