A two-digit number is 63 more than the number formed by interchanging its digits. If the sum of its digits is 9, what is the number?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 81
With tens digit \(a\) and units digit \(b\), the difference of the number and its reverse is \(9(a-b)\); the digit sum gives a second equation.
\(9(a-b)=63\), so \(a-b=7\)
\(a+b=9\)
Adding: \(2a=16\), so \(a=8\) and \(b=1\)
Check: \(81-18=63\)
The number is 81.
Why the other options are incorrect
Option (1) 90 — Incorrect. \(90-09=81\), not 63.
Option (2) 72 — Incorrect. \(72-27=45\), not 63.
Option (3) 18 — Incorrect. This is the reversed number; it is 63 less than the number, not more.