The age of two people has the ratio of 6:5 and by adding ages we get 44, after…
2025
The age of two people has the ratio of 6:5 and by adding ages we get 44, after how many years the ratio would be 8:7.
- A.
5
- B.
6
- C.
8
- D.
7
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Correct answer: C
Let the ages be 6x and 5x.
Given their sum is 44: 6x + 5x = 44, so 11x = 44 and x = 4.
Present ages: 6x = 24 and 5x = 20.
Let y be the number of years after which the ratio becomes 8:7. Then (24 + y)/(20 + y) = 8/7.
Solve by cross-multiplying:
7(24 + y) = 8(20 + y) → 168 + 7y = 160 + 8y.
Rearrange: 168 − 160 = 8y − 7y → 8 = y.
Therefore y = 8. Check: (24 + 8)/(20 + 8) = 32/28 = 8/7.
Answer: After 8 years the ratio will be 8:7.