Question
Three friends—Arun, Bhavesh,
and Chandan—have different ages. Bhavesh is 9 years younger than Chandan. Find Chandan's current age. Statement I: Five years ago, the ratio of Arun’s age to Bhavesh’s age was 4:5. Statement II: Six years from now, the ratio of Bhavesh's age to Chandan's age will be 3:4. Determine whether the information in the statements is sufficient to find Chandan's present age. The question consists of two statements numbered "l and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.Solution
ATQ,
Let the current ages of 'Arun' and 'Bhavesh' be 'x' years and 'y' years, respectively. Therefore, the current age of 'Chandan' = (y + 9) years.
Statement I: According to this statement: 
Simplifying this equation:
Since we do not have enough information to find 'y', the data in Statement I alone is insufficient to determine Chandan's age.
Statement II: According to this statement, six years from now: 
Simplifying this equation:
So, the present age of 'Chandan' = y + 9 = 21 + 9 = 30 years. Therefore, the information in Statement II alone is sufficient to find Chandan's current age, while the information in Statement I alone is not sufficient.
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