Eight years ago, the ratio of the ages of A and B was 9 : 10. Four years from now, the ratio of their ages will be 12 : 13. If C is 10 years older than A, what is C’s present age (in years)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 54
Take the ages of eight years ago as the unknowns; four years from now is 12 years after that time.
Eight years ago: A \(=9k\), B \(=10k\)
Four years from now: A \(=9k+12\), B \(=10k+12\)
\(\displaystyle \frac{9k+12}{10k+12}=\frac{12}{13}\)
\(13(9k+12)=12(10k+12)\), so \(117k+156=120k+144\) and \(k=4\)
A now \(=9\times4+8=44\) years
C now \(=44+10=54\) years