4. One of the two digits of a two-digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
Let us assume the digit at tens place be x
Then, digit at ones place will be 3x.
Original two-digit number = 10x + 3x
After interchanging the digits, the new number = 30x + x
According to the question,
(30x + x) + (10x + 3x) = 88
⇒ 31x + 13x = 88
⇒ 44x = 88
⇒ x = 2
Original number = 10x + 3x = 13x = 13×2 = 26
Hence, required number is 26.