How Old Will Your Brother Be When You Turn a Certain Age? A Simple Mathematical Puzzle

Have you ever come across this intriguing mathematical problem: 'When I was 2, my brother was half of my age. Now I am 10 years old. How old is my brother now?' It may seem daunting, but with a bit of logical thinking, it’s quite straightforward to solve. Let's break it down and explore a step-by-step solution to uncover the answer hidden in this puzzle.

Step-by-Step Solution

Let's start by defining our known variables:

When you were 2, your brother was half your age, which means he was 1 (2 div; 2 1). Now you are 10 years old, and you need to determine your brother’s current age.

To solve this, we can use the logic of age difference. The age difference between you and your brother remains constant over time. So, we first calculate the age difference:

When you were 2, your brother was 1, so the age difference is 2 - 1 1 year.

Now that you are 10 years old, we can calculate your brother's age by subtracting the age difference from your current age:

Your brother's current age 10 - 1 9 years old.

However, let's examine a few more solutions to better illustrate the problem and prevent confusion.

Common Misconceptions and Clarifications

Not everyone gets the right answer, often because of common misconceptions. Here are some examples of wrong answers and clarifications:

Wrong Answer: 9?

Someone might think your brother is 9 years old. This is incorrect because the puzzle states that when you were 2, your brother was half of your age, which means he was 1. Therefore, the age difference is 1 year, and you are 10 now, making your brother 10 - 1 9. This is correct, but let's summarize it:

Wrong Answer: 19?

Many people incorrectly think the brother is 19. This is wrong because if the brother is 5 years younger than you, the age difference remains constant over time. Since you are 10 now, your brother would still be 5 years younger, making his age 10 - 5 5 14 19. But a simpler way to look at it is just by subtracting the age difference from your age now:

Brother's current age 10 - 5 5 14 19 - 14 19 - 5 14. This is still incorrect, but it helps illustrate the concept.

Further Clarification

Another approach is to consider the age difference between you and your brother. The puzzle states that when you were 2, your brother was 1 (2 div; 2 1). Thus, the age difference is 1 year. When you are 10 now, your brother, being 1 year younger, would be 10 - 1 9. However, if considering a 5-year difference as initially thought, the correct age would be 10 - 5 5 4 9. This is correct.

Conclusion

In conclusion, when you turn 10, your brother would be 5 years younger than you, making his age 10 - 5 9. Understanding this simple mathematical concept helps in solving such puzzles and ensures we avoid common pitfalls that might arise from incorrect assumptions.

Keywords

age calculation, sibling age difference, mathematical puzzle