Question

The sum of the digits of a two- digit number is 13. The number obtained by interchanging it's digits exceeds the given number by 27. Find the original number.​

Answer 1

Answer:

58

Step-by-step explanation:

Let ten's digit be x ,

and unit's digit be y.

Then the number will be 10x +y

When the digits are interchanged , the number becomes : 10y+x

From the given data, x+y = 13    -------------------------------(1)

And (10x+y) + 27 = 10y+x

  => 9x -9y +27 = 0

  =>  y = x +3   --------------------------------(2)

Using (1) and (2),

      x + (x+3) =13

 => 2x = 10

 => x = 5.

Now putting x = 5 in (2), we get

 => y = 5+3=8

 => y = 8.

Therefore, the number is 10x +y = 10(5)+(8)

                                                      = 58.