Question

What is the age difference between Peter and his brother?
I. Peter's age is 3 times his brother's age.
II. The sum of Peter's and his brother's age is 40 years.

• A. If the statement I alone is sufficient to answer the question.
• B. If the statement II alone is sufficient to answer the question.
• C. If the statements I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. If the statements I and II together are not sufficient to answer the question and additional data is required.

Hint:

When solving age-related problems, create variables for the unknowns and use the given conditions to form equations that can be solved algebraically.

Answer 1

The Correct Option is C

Let Peter's age be \( P \) and his brother's age be \( B \). From condition I: Peter's age is 3 times his brother's age. This gives the equation: \[ P = 3B \] From condition II: The sum of their ages is 40 years. \[ P + B = 40 \] Now, substitute \( P = 3B \) into the second equation: \[ 3B + B = 40 \] \[ 4B = 40 \] \[ B = 10 \] Now that we know the brother’s age is 10 years, substitute this back into \( P = 3B \) to find Peter's age: \[ P = 3 \times 10 = 30 \] The age difference between Peter and his brother is: \[ P - B = 30 - 10 = 20 \] Thus, the age difference between Peter and his brother is \( \boxed{20} \) years. Therefore, the correct answer is \( \boxed{3} \).