Question

A two-digit number is 4 times the sum of its digits and twice the product 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 number is 4 times the sum of the two digits. Thus, we have

After interchanging the digits, the number becomes.

The number is twice the product 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 in the second equation, we get

Or

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

Hence, the number is.

Note that the first pair of solution does not give a two digit number.