Question

The sum of digits of a two number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the given 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 15. Thus, we have ` x + y = 15`

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

The number obtained by interchanging the digits is exceeding by 9 from the original number. Thus, we have

`10 x + y = 10y + x +9`

`⇒ 10 x + y - 10 y + x + 9`

` ⇒ 9x - 9 y = 9`

`⇒ 9 ( x - y) = 9`

` ⇒ x - y = 9/9`

` ⇒ x - y = 1`

So, we have two equations 

` x + y = 15`

` x - y = 1`

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)= 15 + 1`

`⇒ x + y + x - y = 16 `

` ⇒ 2 x = 16`

` ⇒ x = 16/2`

` ⇒ x = 8`

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

` 8 + y = 15`

`⇒ y = 15 - 8

` ⇒ y = 7`

Hence, the number is ` 10 xx7 + 8 = 78 .`