Ages (difference now; past ratio given): The difference between the present ages of Arun and Barun is 14 years. Seven years ago, the ratio of their ages was 5 : 7. Find Barun's present age.
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A35 years
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B42 years
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C49 years
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D56 years
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E48 years
Answer
Correct Answer: 56 years
Explanation
Introduction / Context:This problem mixes a present absolute difference with a past ratio, a frequent pattern in age questions. The key is to express present ages from the ratio's time-slice and then align them with today's difference.
Given Data / Assumptions:
- Let present ages be A (Arun) and B (Barun), with B − A = 14 (Barun older, consistent with the 5 : 7 past ratio).
- Seven years ago: (A − 7) : (B − 7) = 5 : 7.
Concept / Approach:Convert the past ratio into an equation and combine with the present difference. Solving the two linear equations yields today's ages directly.
Step-by-Step Solution:
From the ratio: 7(A − 7) = 5(B − 7) ⇒ 7A − 49 = 5B − 35 ⇒ 7A = 5B + 14. Use B = A + 14 in the previous: 7A = 5(A + 14) + 14 = 5A + 70 + 14 ⇒ 2A = 84 ⇒ A = 42. Then B = A + 14 = 56.Verification / Alternative check:Seven years ago: A = 35, B = 49 ⇒ 35 : 49 = 5 : 7 (✓). Difference now 14 (✓).
Why Other Options Are Wrong:All other listed numbers fail either the difference constraint or the reconstructed past ratio when checked.
Common Pitfalls:Applying the 14-year difference to the past snapshot or reversing the elder–younger roles; the ratio 5 : 7 indicates Barun is older.
Final Answer:56 years