Multiple choice

The ratio of present age of two persons, Ryan and Simon is 5 : 8. Which of the following can be the ratio of ages of Ryan and Simon after 12 years?

  1. 1 : 2

  2. 3 : 7

  3. 7 : 9

  4. 9 : 19

  5. 9 : 7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ages be 5x and 8x. After 12 years, the ratio is (5x+12)/(8x+12). Testing the options, for 7:9, (5x+12)/(8x+12) = 7/9 leads to 45x + 108 = 56x + 84, so 11x = 24, which is not an integer. However, checking the ratio 7:9 against the options, it is the only one that could potentially result from an age progression.

AI explanation

Let the present ages of Ryan and Simon be 5x and 8x. After 12 years, their ages will be 5x + 12 and 8x + 12. For their new ratio to be valid, the difference in their ages must remain 3x, so the difference between the numerator and denominator of the correct option must be a multiple of 3. Testing option C gives 9 - 7 = 2, but testing the years reveals (5x + 12) / (8x + 12) = 7 / 9, which solves to 45x + 108 = 56x + 84, yielding 11x = 24 and x = 24/11. Testing all options reveals that only the ratio 7 to 9 allows for a positive real value of x from the equation 45x + 108 = 56x + 84, making 7 to 9 the correct ratio.

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