The sum of the digits of a 2-digit number is 7. If 9 is added to the number, the digits interchange their places. Find the digit at the ten's place of the original number.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
A 2-digit number with tens digit \(a\) and units digit \(b\) is \(10a+b\); with the digits interchanged it is \(10b+a\).
Sum of the digits: \(a+b=7\) (1)
Adding 9 interchanges the digits: \(10a+b+9=10b+a\)
\(9b-9a=9\)
\(b-a=1\) (2)
Subtracting (2) from (1), the \(b\) terms cancel: \(2a=6\), so \(a=3\) (and \(b=4\))
The number is 34, so the tens digit is 3.