Discussion
Sachin is younger than Rahul by 7 years. If the ratio of their ages is 7 : 9, find the age of Sachin.
Answer: A
Sachin is 24.5 years old.
With the ratio 7 : 9, the ages are 7k and 9k, and their difference 2k equals 7 years:
\[ \begin{aligned} 9k - 7k &= 7 \Rightarrow k = 3.5 \\ \text{Sachin} &= 7 \times 3.5 = 24.5 \end{aligned} \]
Rahul is then 31.5, and 24.5 : 31.5 = 7 : 9. The other options give differences that do not match the ratio; 27.5, for example, would make Rahul 34.5, a ratio of about 0.8.
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