A two-digit number is 54 more than the number obtained by interchanging its digits. What is the difference between the two digits of the number?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6
With tens digit \(a\) and units digit \(b\), the number is \(10a+b\) and the reversed number is \(10b+a\). Their difference is always \(9(a-b)\).
\((10a+b)-(10b+a)=9a-9b=9(a-b)\)
\(9(a-b)=54\)
\(a-b=54\div9=6\)
Example: \(71-17=54\)
The digits differ by 6.
Why the other options are incorrect
Option (1) 9 — Incorrect. If the digits differed by 9, the two numbers would differ by \(9\times9=81\), not 54.
Option (2) 4 — Incorrect. If the digits differed by 4, the two numbers would differ by \(9\times4=36\), not 54.
Option (4) 5 — Incorrect. If the digits differed by 5, the two numbers would differ by \(9\times5=45\), not 54.