Three years ago, the ratio of the ages of a mother and her daughter was 8 : 3. After four years, their ages will be in the ratio 11 : 5. What is the present age of the mother (in years)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 51
Write the ages of three years ago with one unknown; four years from now each is 7 years older than then.
Three years ago: mother \(=8k\), daughter \(=3k\) years
After four years: \(\displaystyle \frac{8k+7}{3k+7}=\frac{11}{5}\)
\(5(8k+7)=11(3k+7)\), so \(40k+35=33k+77\) and \(k=6\)
Mother now \(=8\times6+3=51\) years