Present ratio of ages is 2 : 3 (A : B). Five years hence, the ratio will be 3 : 4. What is A’s present age?

Introduction / Context:
We are given present and future age ratios. Represent the present ages using a single parameter and impose the future ratio after adding 5 years to both ages. Solve for the parameter to find A’s age.

Given Data / Assumptions:

• Now: A : B = 2 : 3 ⇒ A = 2x, B = 3x.
• After 5 years: (A + 5) : (B + 5) = 3 : 4.
• Find A’s present age.

Concept / Approach:
Use cross-multiplication on the future ratio to get a linear equation in x. Compute A = 2x.

Step-by-Step Solution:

Verification / Alternative check:

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Final Answer:
10 years