Single correct option
The present ages of A and B are in the ratio 3 : 4. Eight years ago, the ratio of their ages was 5 : 7. What is the sum of their present ages (in years)?
- A. 96
- B. 112
- C. 120
- D. 128
Show answer and solution
Answer: (B) 112
Let the present ages be 3k and 4k. Eight years ago: (3k − 8)/(4k − 8) = 5/7.
Cross-multiplying: 21k − 56 = 20k − 40 ⇒ k = 16.
Present ages: 48 and 64, sum = 112.
Check: 40 : 56 = 5 : 7 ✓.
Tip: The difference in ages stays constant: k (in 3k:4k) must also equal 2m (in 5m:7m) and 3k − 8 = 5m gives the same result quickly.
Cross-multiplying: 21k − 56 = 20k − 40 ⇒ k = 16.
Present ages: 48 and 64, sum = 112.
Check: 40 : 56 = 5 : 7 ✓.
Tip: The difference in ages stays constant: k (in 3k:4k) must also equal 2m (in 5m:7m) and 3k − 8 = 5m gives the same result quickly.
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