Multiple choice

The age of Sulekha and Arunima are in the ratio $9:8$ respectively. After $5$ years, the ratio of their ages will be $10:9$. What is the difference between their ages?

  1. $4$ years
  2. $5$ years
  3. $6$ years
  4. $7$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let ages be 9x and 8x. (9x+5)/(8x+5) = 10/9. Cross-multiplying: 81x + 45 = 80x + 50, so x = 5. The difference is 9x - 8x = x = 5 years.

AI explanation

Let the present ages of Sulekha and Arunima be 9x and 8x respectively. After 5 years, the ratio becomes (9x + 5) / (8x + 5) = 10 / 9, so by cross multiplication we get 81x + 45 = 80x + 50. Solving this gives x = 5, making the present ages 45 years and 40 years respectively. The difference between their ages is therefore 5 years.

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