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.
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A35 years
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B30 years
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C25 years
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D18 years
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E40 years
Answer
Correct Answer: 35 years
Explanation
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:
3x − 10 = (1/2)(4x − 10) = 2x − 5. Thus x = 5 ⇒ D = 15, N = 20. Sum of present ages = 15 + 20 = 35 years.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