Question

The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, 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 two digits of the number are differing by 3. Thus, we have

After interchanging the digits, the number becomes.

The sum of the numbers obtained by interchanging the digits and the original number is 99. Thus, we have

So, we have two systems of simultaneous equations

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

(i) First, we solve the system

Adding the two equations, we have

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

Hence, the number is.

(ii) Now, we solve the system

Adding the two equations, we have

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

Hence, the number is.

Note that there are two such numbers.