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Question
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.
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