Eight years ago, the ratio of the ages of A and B was 2 : 3. Four years ago, the ratio of their ages was 5 : 7. What will be the ratio of their ages 8 years from now?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 : 5
Take the ages eight years ago as \(2k\) and \(3k\). Four years later each is 4 years older, and these ages are in the ratio 5 : 7.
\(\displaystyle\frac{2k+4}{3k+4}=\frac{5}{7}\)
\(14k+28=15k+20\), so \(k=8\)
Present ages: A \(=16+8=24\) years, B \(=24+8=32\) years
After 8 years: \(32:40=4:5\)