Question

A is 3 years younger than C but one year older than D. D is one year older than B but 4 years younger than C. C is 15 years old. What is the age of B in years?

• A. \( 13 \)
• B. \( 12 \)
• C. \( 11 \)
• D. \( 10 \)

Hint:

\textbf{Age-Related Problems.} When solving problems involving ages and relationships between them, it is helpful to translate the given statements into algebraic equations. By substituting the known values, you can systematically find the unknown ages.

Answer 1

The Correct Option is D

We are given the following information about the ages of A, B, C, and D: (A) A is 3 years younger than C. (B) A is one year older than D. (C) D is one year older than B. (D) D is 4 years younger than C. (E) C is 15 years old. We need to find the age of B. Let's use the given information step by step: From statement 5, we know that the age of C is 15 years. From statement 1, A is 3 years younger than C: Age of A \( = \text{Age of C} - 3 = 15 - 3 = 12 \) years. From statement 2, A is one year older than D: Age of D \( = \text{Age of A} - 1 = 12 - 1 = 11 \) years. We can verify this with statement 4, D is 4 years younger than C: Age of D \( = \text{Age of C} - 4 = 15 - 4 = 11 \) years. This is consistent. Now, from statement 3, D is one year older than B: Age of B \( = \text{Age of D} - 1 = 11 - 1 = 10 \) years. Therefore, the age of B is 10 years.