Question : 2 years ago, the ratio of X and Y's age was 7 : 5 and after 2 years their age will be in the ratio 9 : 7. What is the present age of Y?
Option 1: 18 years
Option 2: 12 years
Option 3: 16 years
Option 4: 14 years
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Correct Answer: 12 years
Solution : 2 years ago, the ratio of X and Y's ages was 7 : 5. So, Let 2 years ago X's age was $7k$ and Y's age was $5k$. According to the question, $\frac{7k+4}{5k+4}=\frac{9}{7}$ $⇒49k+28=45k+36$ $⇒4k=8$ $⇒k=2$ So, 2 years ago Y's age $=5k=5×2=10$ $\therefore$ Y's present age $=10+2=12$ years Hence, the correct answer is 12 years.
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