Multiple choice

The ages of Rahul and Ramya are in the ratio of 7:3 respectively. After 6 years, the ratio of their ages will be 5:3. What is the difference in their ages?

  1. 6 years

  2. 10 years

  3. 12 years

  4. 8 years

  5. None of these
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D Correct answer
Explanation

Let ages be 7x and 3x. (7x+6)/(3x+6) = 5/3. 21x + 18 = 15x + 30. 6x = 12, so x = 2. Ages are 14 and 6. Difference is 8.

AI explanation

Let the present ages of Rahul and Ramya be 7x and 3x. After 6 years, the ratio 7x plus 6 to 3x plus 6 equals 5 to 3. Cross multiplying gives 21x plus 18 equals 15x plus 30, so 6x equals 12 and x equals 2. The difference in their ages is 7x minus 3x, which is 4x, making the difference 4 times 2, or 8 years.

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