Question

The sum of the digits of a 2-digit number is 11. The number obtained by interchanging the digits exceeds the original number by 27. Find the number.​

Answer 1

Answer:

Let’s represent the tens digit with ‘a,” and the ones digit with ‘b.’

The value of this number is 10a + b; this number is 27 more than the number formed by the same digits in the other order, so 10a + b = 10b + a + 27.

The digit sum is 11; a + b=11, or b = 11 - a.

10a + b = 10b + a + 27

10a + (11 - a) = 10(11 - a) + a + 27

10a + 11 - a = 110 - 10a + a + 27

9a + 11 = 110 - 9a + 27

9a + 11 = 137 - 9a

18a + 11 = 137

18a = 126

a = 126/18

a = 7

b = 11 - 7 = 4

So the original number is 74.

The sum of the digits is 7+4=11.

And if you reverse the digits you get 47; 47 + 27 = 74.