Question

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find 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.

The sum of the two digits of the number is 9. Thus, we have

After interchanging the digits, the number becomes.

Also, 9 times the number is equal to twice the number obtained by reversing the order of the digits. Thus, we have

So, we have the systems of equations

Here x and y are unknowns. We have to solve the above systems of equations for x and y.

Substituting from the second equation to the first equation, we get

Substituting the value of y in the second equation, we have

Hence, the number is.