Solving the Age Puzzle: When I Was 20, My Brother Was Half My Age

The age puzzle you presented is a classic mathematical problem that involves understanding the concept of age differences and how they remain constant over time. Let us break down the problem to understand the solution clearly.

The Problem

When I was 20, my brother was half my age. Now I am 50. How old will my brother be?

The Detailed Solution

Initially, your brother was half your age when you were 20. This means he was 10 years old:

Step 1: Initial Age Calculation

When you were 20:

Your brother's age 20 / 2 10

Step 2: Age Difference

The age difference between you and your brother is always 10 years. This is a key observation in solving the problem, as it remains constant over time:

Your age - Brother's age 20 - 10 10 years difference

Step 3: Applying the Difference to the Current Age

Now that you are 50, let's apply the 10-year difference to find your brother's current age:

Brother's age Your current age - 10

Brother's age 50 - 10 40

A Simple Breakdown

Another way to look at the problem is to break it down step-by-step:

Step 1: Calculate Brother's Age When You Were 20

Your brother was 10 years old when you were 20.

Step 2: Calculate the Age Difference

The age difference remains constant at 10 years.

Step 3: Calculate Your Brother's Current Age

Since the age difference is 10 years, subtract 10 from your current age (50) to find your brother's age:

Your brother is now 50 - 10 40 years old.

Conclusion

Therefore, if you are currently 50, your brother, who was half your age when you were 20, is now 40 years old.

Related Key Concepts

The math puzzle you described touches on some key mathematical concepts:

Age Difference

The age difference between two people remains constant over time. If one person is always half the age of the other, the difference can be calculated and applied at any point in time.

Mathematical Puzzles

Puzzles like this one engage the mind in logical and mathematical reasoning, making them both fun and educational.

Age Problems

Solving age-related problems often involves basic arithmetic and a clear understanding of the concept of age differences.

To further explore and solve similar puzzles, you can practice with various age-related problems and use mathematical principles to derive solutions.