Question

A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. 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 number is 4 more than 6 times the sum of the two digits. Thus, we have

After interchanging the digits, the number becomes.

If 18 is subtracted from the number, the digits are reversed. 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.

Multiplying the second equation by 5 and then subtracting from the first, we have

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

Hence, the number is.