Multiple choice

5 years ago, the ratio of the ages of A and B was 3 : 2 and 5 years hence, their ages will be in the ratio of 5 : 4. What is the sum of present ages of A and B?

  1. 30 years

  2. 35 years

  3. 40 years

  4. 45 years

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let present ages be A and B. 5 years ago: (A-5)/(B-5) = 3/2. 5 years hence: (A+5)/(B+5) = 5/4. Cross-multiplying: 2A-10 = 3B-15 → 2A-3B = -5; 4A+20 = 5B+25 → 4A-5B = 5. Solving: multiply first by 2: 4A-6B = -10. Subtract from second: (4A-5B) - (4A-6B) = 5 - (-10) → B = 15. Then 2A-3(15) = -5 → 2A = 40 → A = 20. Sum = 35.

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