Question

The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?

Answer 1

Let the digits at units and tens place of the given number be x and y respectively. Thus, the number is `10 y + x.`.

The sum of the digits of the number is 13. Thus, we have  ` x + y =13`

After interchanging the digits, the number becomes `10 x + y`.

The difference between the number obtained by interchanging the digits and the original number is 45. Thus, we have

`(10 x + y) - (10 y + x)= 45`

`⇒ 10 x + y -10 y -x = 45`

` ⇒ 9 x - 9y = 45`

`⇒ 9(x - y) = 45`

`⇒ x - y = 45/9`

`⇒ x - y = 5`

So, we have two equations

` x + y = 13`

` x - y = 5`

Here x and y are unknowns. We have to solve the above equations for x and y.
Adding the two equations, we have

`( x + y) + ( x - y )= 13 + 5`

`⇒ x + y + x - y = 18`

` ⇒ 2x = 18`

` ⇒ x = 18/2`

`⇒ x = 9`

Substituting the value of x in the first equation, we have

` 9 + y = 13`

` ⇒ y = 13 - 9`

` ⇒ y = 4`
Hence, the number is ` 10 xx4 + 9 = 49 .`