Age ratios then and later: Two brothers currently have ages in the ratio 1 : 2. Five years ago the ratio was 1 : 3. What will be their age ratio after 5 years from now?

Introduction / Context:
Age-ratio problems are solved by translating ratios into linear equations for actual ages. Once present ages are known, future ratios are straightforward. This checks comfort with setting up ratio equations at different time points.

Given Data / Assumptions:

• Let present ages be x and 2x (older is 2x).
• Five years ago: (x − 5) : (2x − 5) = 1 : 3.
• We seek (x + 5) : (2x + 5).

Concept / Approach:
Solve the past-ratio equation for x, then compute the ages after 5 years and simplify the ratio to lowest terms.

Step-by-Step Solution:

Verification / Alternative check:
Check the given past ratio: 5 years ago they were 5 and 15, which is indeed 1 : 3.

Why Other Options Are Wrong:
1:4, 2:3, 5:6 are not the simplified ratio of 15:25.

Common Pitfalls:
Using the same ratio across time points without solving for actual ages first. Ratios typically change as equal years are added or subtracted.

Final Answer:
3 : 5