Multiple choice

The ratio of the present ages of A and B is 8 : 6, respectively. The ratio of A's age 5 years ago to B's age 5 years hence is 1 : 1. What is the ratio of A's age 5 years hence to B's age 5 years ago?

  1. 9 : 5

  2. 4 : 3

  3. 5 : 9

  4. 5 : 2

  5. 7 : 6
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A Correct answer
Explanation

Let A=8x, B=6x. (8x-5)/(6x+5) = 1/1, so 8x-5 = 6x+5, 2x=10, x=5. Present ages: A=40, B=30. A+5 = 45, B-5 = 25. Ratio 45:25 = 9:5.

AI explanation

Let the present ages of A and B be 8x and 6x; the given condition states that (8x - 5) / (6x + 5) = 1. Solving 8x - 5 = 6x + 5 gives 2x = 10, so x = 5. The required ratio of A's age 5 years hence to B's age 5 years ago is (8x + 5) : (6x - 5), which becomes 45 : 25 or 9 : 5.

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