The difference between a two-digit number and the number obtained by interchanging its digits is 27. What is the difference between the digits of the number?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 3
A two-digit number with tens digit \(a\) and units digit \(b\) is \(10a+b\); interchanging the digits gives \(10b+a\). Their difference is always 9 times the difference of the digits.
\((10a+b)-(10b+a)=9a-9b=9(a-b)\)
\(9(a-b)=27\)
\(a-b=3\)
For example, \(52-25=27\). The difference between the digits is 3.