The ratio of the ages of A and B is 10 : 13. The ratio of A's age ten years ago to B's age ten years hence is 8 : 15. Find the ratio of A's age ten years hence to B's age ten years ago.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 12 : 11
Write the present ages with one unknown from the first ratio, then use the second ratio to find that unknown.
Let the present ages be A \(=10x\) and B \(=13x\)
\(\displaystyle \frac{10x-10}{13x+10}=\frac{8}{15}\)
\(15(10x-10)=8(13x+10)\), so \(150x-150=104x+80\)
\(46x=230\), so \(x=5\)
A \(=50\) years, B \(=65\) years
A ten years hence \(=60\); B ten years ago \(=55\)
Ratio \(=60:55=12:11\)