The ratio of the ages of X and Y is 6 : 5. Four years ago, the ratio was 5 : 4. What will be the ratio of the ages of X and Y after 16 years?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10 : 9
Write the present ages with one unknown from the first ratio, and use the ratio of four years ago to find it.
Let X \(=6k\) and Y \(=5k\) years
\(\displaystyle \frac{6k-4}{5k-4}=\frac{5}{4}\)
\(4(6k-4)=5(5k-4)\), so \(24k-16=25k-20\) and \(k=4\)
X \(=24\) years, Y \(=20\) years
After 16 years: \(40:36=10:9\)