A says, “If you reverse the digits of my age, you get my brother’s age. He is older than me, and the difference between our ages is one-eleventh of the sum of our ages.” What is the age of A’s brother?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 54 years
A two-digit age with tens digit \(x\) and units digit \(y\) is \(10x+y\); reversing the digits gives \(10y+x\).
A \(=10x+y\), brother \(=10y+x\), with \(y\) greater than \(x\) since the brother is older
Difference \(=9(y-x)\); sum \(=11(x+y)\)
\(\displaystyle 9(y-x)=\frac{11(x+y)}{11}=x+y\), so \(8y=10x\), that is \(4y=5x\)
Digits from 1 to 9 allow only \(x=4,\ y=5\)
A \(=45\) years, brother \(=54\) years