Question

The sum of the digits of a two digit number is 13 the number obtained by interchanging the digits of the given number exceeds that number by 27 find the number

Answer 1

Let the tens place digit be a

And unit place digit be b

According to first condition,

a + b = 13 -----(1)

According to second condition,

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

=> 10b + a - 10a - b = 27

=> 9b - 9a = 27

=> b - a = 3 ------(2)

On adding equation 1 and 2, we get

2b = 16

=> b = 8

Now,

On substituting the value of b in equation 1, we get

a + 8 = 13

=> a = 5

Number = 58

Answer 2

Let the digit at ten's place be x.

Let the digit at unit's place be y.

Therefore the original number is 10x + y  -------- (*)

On interchanging the original number, we get 10y + x.

Given that sum of digits of a two digit number is 13.

= > x + y = 13.  ------ (1)


Given that the number obtained by interchanging the digits of the given number exceeds that number by 27.

= > 10y + x = 10x + y + 27

= > 9y - 9x = 27

= > y - x = 3  ------ (2)


On solving (1) & (2), we get

= > x + y = 13

= > -x + y = 3

       ---------------

            2y = 16

               y = 8.



Substitute y = 8 in (1), we get

= > x + y = 13

= > x + 8 = 13

= > x = 13 - 8

= > x = 5.


Substitute x = 5 and y = 8 in (*), we get

= > The original number = 10x + y

                                         = 10(5) + 8

                                          = 50 + 8

                                          = 58.



Therefore the number is 58.


Hope this helps!