A girl is 12 years old and her brother is twice her age. When the girl is 50 years old, how old will her brother be?
The Correct Answer and Explanation is:
To solve this problem, we need to determine the age of the girl’s brother when she is 50 years old, given that the brother is twice her age now.
Step 1: Identify the ages now
- The girl is currently 12 years old.
- Her brother is twice her age. Therefore, the brother’s current age is:
[
2 \times 12 = 24 \text{ years old}
]
Step 2: Determine the age difference
The key to solving the problem is recognizing that the age difference between the girl and her brother remains constant over time. Currently:
- The brother is 24 years old.
- The girl is 12 years old.
The age difference is:
[
24 – 12 = 12 \text{ years}
]
So, the brother is 12 years older than the girl.
Step 3: Project into the future
The problem asks for the brother’s age when the girl is 50 years old. Since we know the brother is always 12 years older than the girl, we can calculate the brother’s age by adding this 12-year difference to her future age of 50:
[
50 + 12 = 62 \text{ years old}
]
Conclusion
When the girl is 50 years old, her brother will be 62 years old.
Explanation of the concept:
This problem is based on the concept of a constant age difference between two individuals. Since the brother is always 12 years older than his sister, no matter how much time passes, this difference will not change. The relationship between their ages today and in the future depends only on this fixed gap. Even though the brother was twice her age when she was 12, as time progresses, the multiplicative relationship doesn’t stay the same, but the age gap remains constant. Therefore, when the girl turns 50, the brother, being 12 years older, will be 62.