Multiple choice

The ratio of present ages of Jack and John is 2 : 5. The ratio of Jack's age after 3 years to John's age 3 years ago is 1 : 2. What is the ratio of Jack's age 3 years ago to John's age 3 years hence?

  1. 3 : 13

  2. 4 : 15

  3. 5 : 16

  4. 6 : 19

  5. 7 : 15
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C Correct answer
Explanation

Let Jack's age be 2x and John's be 5x. Given (2x + 3) / (5x - 3) = 1 / 2, we get 4x + 6 = 5x - 3, so x = 9. Present ages are 18 and 45. Jack's age 3 years ago was 15, and John's age 3 years hence is 48. The ratio 15:48 simplifies to 5:16.

AI explanation

Let the present ages of Jack and John be 2x and 5x respectively. The ratio of Jack's age after 3 years to John's age 3 years ago is 1:2, giving the equation (2x + 3) / (5x - 3) = 1/2. Cross-multiplying yields 4x + 6 = 5x - 3, so x equals 9, meaning their present ages are 18 and 45. Jack's age 3 years ago was 15, and John's age 3 years hence will be 48, making the ratio 15 to 48, which simplifies to 5 : 16.

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