Ages (past half relation and present ratio): Ten years ago, Divya's age was half of Namrata's. Today their ages are in the ratio 3 : 4. Find the sum of their present ages.

Introduction / Context:
This problem links a past proportional statement with a present ratio. Expressing present ages using a single parameter lets us translate the “ten years ago” condition into a solvable equation.

Given Data / Assumptions:

• Present ratio Divya : Namrata = 3 : 4 ⇒ D = 3x, N = 4x.
• Ten years ago: D − 10 = (1/2)(N − 10).

Concept / Approach:
Substitute D = 3x and N = 4x into the past relation and solve for x. Then compute present ages and sum them to answer the question.

Step-by-Step Solution:

Verification / Alternative check:
Ten years ago they were 5 and 10 respectively, so Divya was indeed half of Namrata (✓). The present ratio 15 : 20 reduces to 3 : 4 (✓).

Why Other Options Are Wrong:
Each alternative sum implies a value of x that breaks either the past “half” relation or the present ratio.

Common Pitfalls:
Misapplying the half relation to the present instead of to the past snapshot, or mixing the ten-year adjustment asymmetrically.

Final Answer:
35 years