One of the two digits of a two digit number is three times the other digit. If you interchange the digit of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

#### Solution

Let the digits at tens place and ones place be x and 3x respectively.

Therefore, original number = 10x + 3x = 13x

On interchanging the digits, the digits at ones place and tens place will be x and 3x respectively.

Number after interchanging = 10 × 3x + x = 30x + x = 31x

According to the given question,

Original number + New number = 88

13x + 31x = 88

44x = 88

Dividing both sides by 44, we obtain

x = 2

Therefore, original number = 13x = 13 × 2 = 26

By considering the tens place and ones place as 3x and x respectively, the two-digit number obtained is 62.

Therefore, the two-digit number may be 26 or 62.