Ratio and Proportion

Concept:Use a common variable to represent ages from the given ratio.Explanation:Let present ages of A and B be $3x$ and $x$ years respectively.After 15 years, A’s age becomes $3x+15$, and B’s age becomes $x+15$.The new ratio is $2:1$, so $\frac{3x+15}{x+15} = \frac{2}{1}$.Cross-multiplying gives $3x+15 = 2(x+15)$.Simplify: $3x+15 = 2x+30$, hence $x = 15$.Therefore, A’s present age = $3 \times 15 = 45$ years, B’s present age = $15$ years.Answer:45 years and 15 years, which matches option B.