Solving the Age Puzzle: When You Were 24, Your Sister Was Half Your Age, Now You’re 48 - What’s Her Age?

Have you ever stumbled upon a math problem that seemed like a riddle or puzzle? The age-related question below is one such classic. Did it leave you puzzled, like many others have? Let’s dive into the details and unravel the mystery.

The Age Puzzle

When you were 24 years old, your sister was half your age. Now you’re 48. How old is she?

Breakdown and Solution

First, let's define the variables and understand the relationship between your age and your sister's age:

Setting the Ages

You are 24 years old, which we will denote as x 24. Let the age of your sister at that time be y years.

Age Difference Relation

The problem states that your sister’s age is 3/4th of your age. So, the relationship can be written as:

y (3/4) * x

Substituting the value of x (24) in the equation, we get:

y (3/4) * 24 18

So, when you were 24, your sister was 18 years old.

Calculating the Age Difference

The difference in your age and your sister's age is:

(x - y) 24 - 18 6 years

This difference will remain the same throughout your lifetimes because both of you grow at the same rate.

Now, Let's Find Your Sister's Age When You’re 48

If you are 48 years old now, and the age difference is 6 years, then:

Your sister’s age will be:

48 - 6 42 years old.

So, when you are 48, your sister will be 42 years old.

Simpler Approach

Alternatively, you can simplify the process by directly using the initial age and the age difference:

Direct Calculation

If you were 24 and your sister was 18 (a 6-year difference), and now you are 48, then:

Your sister’s age can be found as:

48 - 6 42 years.

Or, if you prefer a general formula:

Your sister's age Your age - Age difference.

Another Approach to Solve the Problem

Another way to solve this problem is to calculate the age difference at a different point in time and then apply it to your current age. For example:

Age Difference at 18

If you were 18 and your sister was half your age, then your sister was 9 years old (18/2 9). There’s a 9-year difference between your ages.

Now, if you are 82, and the age difference remains the same, then:

Your sister’s age would be:

82 - 9 73 years old.

So, even another way of solving it would give you the same conclusion that your sister is 73 years old.

Common Pitfalls and Quick Tips

It’s important to avoid common misconceptions. Some people might mistakenly think that the sister's age is half of your current age (82/2 41), which is incorrect because the age increases linearly.

A good quick tip is to always consider the constant age difference and apply it to your current age.

Are you still confused? Don’t hesitate to ask your sister or any friend who might know! It’s often the easiest and most straightforward solution.

In conclusion, the correct answer to the question - When you were 24, your sister was half your age, and now you’re 48, what is her age? - is 42.