Question

The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.

Answer 1

Let the units digit of the original number be x and the tens digit of the original number be 9-x.

The original number in expanded notation is,

= 10(9 - x) + 1 × x

= 90 - 10x + x

= 90 - 9x

On interchanging the digits, the units digit is now 9 - x and the tens digit is now x.

The number obtained by interchanging the digits in expanded notation is,

= 10x+1×(9-x)

= 10x + 9 - x

= 9x + 9

Applying the given condition
9x + 9 - (90 - 9x) = 27

9x + 9 - 90 + 9x = 27

18x - 81 = 27

18x = 27 + 81

18x = 108

x = $\frac{108}{18}$

x = 6

Hence, the units digit; x = 6.

the tens digit = 9 - x = 9 - 6 = 3.

So, the original number is 36.