The Mathematical Puzzle: Finding the Age Difference Between Siblings

Recently, a fascinating mathematical challenge has been circulating online, captivating many individuals who enjoy puzzling their minds. The problem revolves around a brother's and sister's ages relative to each other. Here, we will delve into the solution to this intriguing puzzle and explore the underlying mathematical principles.

Understanding the Puzzle

The problem states that when the sister was 12 years old, her brother was half her age. The question then asks for the sister's current age if her brother is now 32.

Solving the Mathematical Puzzles

Let's break down the solution step by step using a logical and mathematical approach:

When the sister was 12, the brother was 6: According to the problem, the brother was half the sister's age. Therefore, if the sister was 12, the brother must have been 6. The sister is always 6 years older than her brother: Since the brother was 6 when the sister was 12, it means the sister is 6 years older than her brother. This age difference is constant and does not change as they grow older. Calculating the sister's current age: Now, we know the brother's current age is 32. Since the sister is 6 years older, her current age would be 32 6 38.

Alternative Solutions and Debates

The puzzle can also be solved using different methods, leading to lively debates on the accuracy of each approach. Here are a few alternative methods:

Using a ratio approach: Some might argue that the brother is 5/6 of the sister's current age. If the brother is 32, and 32 is 5/6 of the sister's age, we can find the sister's age by multiplying 32 by 6/5, resulting in 38.4. Thus, rounding to the nearest whole number, the sister is 38 years old. Adding years: Another approach is to note that the sister was 10 and the brother was 5. They are always 5 years apart. Since the brother is now 32, subtracting 5 would give the sister's age, which is 32 - 5 27. This method, however, misinterprets the initial condition and leads to an incorrect answer. Using algebra: Let's denote the sister's current age as Y and the brother's current age as B. According to the problem, Y - B 6, and B 32. Substituting B into the equation, we get Y - 32 6, which simplifies to Y 32 6 38. This method is mathematically sound and accurate.

Conclusion

The correct answer to the puzzle is that the sister is 38 years old, and the brother is 32 years old. The puzzle illustrates the importance of accurately interpreting mathematical conditions and using consistent logical reasoning.

Understanding such puzzles not only maintains our intellectual engagement but also reinforces the fundamental principles of mathematics. Whether you enjoy mathematical puzzles for personal interest or as a means of enhancing your problem-solving skills, they provide a fun and enlightening experience.