Multiple choice

If the ratio of the ages of A and B is 3 : 5 and after six years, the ratio of their ages becomes 2 : 3, then what is the difference of their ages?

  1. 10

  2. 16

  3. 12

  4. 24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ages be 3x and 5x. After 6 years, (3x + 6) / (5x + 6) = 2/3. 9x + 18 = 10x + 12, so x = 6. The difference in ages is 5x - 3x = 2x = 2 * 6 = 12.

AI explanation

Let the present ages of A and B be 3x and 5x respectively. After 6 years, their ages are 3x + 6 and 5x + 6, and setting the ratio to 2:3 gives the equation (3x + 6) / (5x + 6) = 2 / 3. Cross-multiplying yields 9x + 18 = 10x + 12, which solves to x = 6. The difference between their ages is 5x - 3x = 2x, so 2 * 6 = 12.

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