Question

Alex has two children - Ben and Chloe. The current age of Alex is 4 times that of Ben. 4 years later, the age of Alex is 4 times that of Chloe. What is the age difference between Ben and Chloe?

• A. 2
• B. 3
• C. 4
• D. 5
• E. 6

Hint:

In age problems, clearly define your variables (e.g., A = Alex's current age). Be careful when dealing with future or past ages; always add or subtract the time period from the current age of each person involved.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a word problem involving ages. The key is to translate the given statements into algebraic equations and solve them simultaneously to find the required value.
Step 2: Detailed Explanation:
Let A, B, and C be the current ages of Alex, Ben, and Chloe, respectively.
From the first statement: "The current age of Alex is 4 times that of Ben."
\[ A = 4B \quad \text{(Equation 1)} \] From the second statement: "4 years later, the age of Alex is 4 times that of Chloe."
In 4 years, Alex's age will be \(A + 4\).
In 4 years, Chloe's age will be \(C + 4\).
So, the equation is: \[ A + 4 = 4(C + 4) \] \[ A + 4 = 4C + 16 \] \[ A = 4C + 12 \quad \text{(Equation 2)} \] Now we have two expressions for Alex's current age, A. We can set them equal to each other.
From Equation 1 and Equation 2: \[ 4B = 4C + 12 \] We need to find the age difference between Ben and Chloe, which is \(B - C\) (assuming Ben is older, which the equation suggests).
Divide the entire equation by 4: \[ \frac{4B}{4} = \frac{4C}{4} + \frac{12}{4} \] \[ B = C + 3 \] Step 3: Final Answer:
Rearranging the equation, we get: \[ B - C = 3 \] The age difference between Ben and Chloe is 3 years.