Solved UPSC CDS/OTA Question
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Q · AgeModerate · 45s
The ratio of present ages of A and B is 5:7. After 6 years, the ratio becomes 3:4. Find the present age of A.
TopicAge
Question Typemultiple choice
DifficultyModerate
Marking+1 / −0.33
From TestChapter Test 1 (Chapter Test)
Test Duration30 min
Step-by-Step Solution
The complete worked solution.
Every step explained - no skipped algebra.
Let present ages be:
A = 5x
B = 7x
After 6 years:
A’s age = 5x + 6
B’s age = 7x + 6 Ratio: (5x + 6)/(7x + 6) = 3/4
Cross-multiply: 4(5x + 6) = 3(7x + 6) → 20x + 24 = 21x + 18 → 20x – 21x = 18 – 24 → –x = –6 → x = 6
Now find A’s age: A = 5x = 5 × 6 = 30 years
Final Answer: Option B - 30 years