Difficulty: Medium
Correct Answer: 24.5 years
Explanation:
Introduction / Context:
This question combines a ratio of ages with an absolute difference between two people, Sachin and Rahul. We use these two conditions together to find Sachin s exact age.
Given Data / Assumptions:
Concept / Approach:
Let Sachin s age be 7k and Rahul s age be 9k to match the ratio 7 : 9. The difference between their ages is then 9k - 7k = 2k. The statement that Sachin is 7 years younger than Rahul means this difference must be 7. Hence 2k = 7, which allows us to determine k and then compute Sachin s age.
Step-by-Step Solution:
Let Sachin s present age = 7k.
Let Rahul s present age = 9k.
Age difference Rahul - Sachin = 9k - 7k = 2k.
Given that Sachin is 7 years younger, so 2k = 7.
Thus k = 7 / 2 = 3.5.
Sachin s age = 7k = 7 * 3.5 = 24.5 years.
Rahul s age = 9k = 9 * 3.5 = 31.5 years.
The key answer required is that Sachin is 24.5 years old.
Verification / Alternative check:
Check the conditions. The ratio Sachin : Rahul is 24.5 : 31.5. Dividing both by 3.5 gives 7 : 9, matching the given ratio. The difference Rahul - Sachin is 31.5 - 24.5 = 7 years, which matches the statement that Sachin is 7 years younger than Rahul. Therefore the solution is consistent.
Why Other Options Are Wrong:
If Sachin were 25.5, 26.5 or 27.5 years old, the corresponding Rahul ages required to maintain the 7 : 9 ratio would not give a fixed difference of exactly 7 years. These values do not satisfy both the ratio and the difference conditions simultaneously.
Common Pitfalls:
Some students try to guess by trial rather than setting up the algebra, which can be slow and error prone. Others incorrectly interpret the ratio as Rahul : Sachin, or forget that the difference must be exactly 7. Using the standard approach of expressing ages as multiples of the ratio numbers helps keep the reasoning clear.
Final Answer:
Sachin s present age is 24.5 years.
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