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
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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