Question

A is three years older than B who is twice as old as C. If the sum of the ages of A, B and C is 28 years, then how old is B?

• A. 7 years
• B. 8 years
• C. 9 years
• D. 10 years

Hint:

Translate word problems into algebraic equations step-by-step using variables for unknowns. Keep track of relationships like "older than" or "twice as old".

Answer 1

The Correct Option is D

Let C's age be \( x \) years. Then, - B = \( 2x \) (since B is twice as old as C) - A = \( 2x + 3 \) (A is 3 years older than B) Now, sum of their ages: \[ A + B + C = (2x + 3) + 2x + x = 5x + 3 \] Given: \[ 5x + 3 = 28 \Rightarrow 5x = 25 \Rightarrow x = 5 \] So, - B = \( 2x = 10 \) years