Multiple choice

Some years ago, Neha was as old as Karan is now. At that time, the ratio of Neha's age to Karan's age was 8 : 7. In the future, when Karan reaches Neha's current age, what will be the ratio of their ages at that time?

  1. 4 : 3

  2. 5 : 4

  3. 8 : 7

  4. 10 : 9

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Neha's age be N and Karan's be K. The age difference D = N - K is constant. When Neha was K, the ratio was 8:7, so (K - D)/K = 8/7. Since D = N - K, we have (2K - N)/K = 8/7, leading to 14K - 7N = 8K, or 6K = 7N. Solving for the future ratio when Karan is N yields 10:9.

AI explanation

Let the constant age difference between Neha and Karan be y years, with Neha being older. Some years ago, Neha was as old as Karan is now, meaning Neha's present age is Karan's present age plus y; at that past time, the ratio of Neha's age to Karan's age was 8 to 7, so Karan's present age equals 8y. In the future, when Karan reaches Neha's present age of 8y plus y, which is 9y, Neha will be 9y plus y, which is 10y. The ratio of their ages at that future time will be 10y divided by 9y, which is 10 to 9.

Keep practicing — related questions