When their son was born, the ratio of the ages of the father and the mother was 11 : 10. When the son is 4 times his present age, the ratio of the ages of the father and the mother will be 19 : 18. What is the ratio of the present ages of the father and the mother?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 13 : 12
Measure every time from the son’s birth: if the son is \(s\) years old now, then now is \(s\) years after his birth, and the later time is \(4s\) years after his birth.
At the son’s birth: father \(=11k\), mother \(=10k\)
When the son is \(4s\): \(\displaystyle \frac{11k+4s}{10k+4s}=\frac{19}{18}\)
\(18(11k+4s)=19(10k+4s)\), so \(198k+72s=190k+76s\)
\(8k=4s\), so \(s=2k\)
Now: father \(=11k+2k=13k\), mother \(=10k+2k=12k\)
Ratio of present ages \(=13:12\)