Multiple choice

The present ages of Samir and Tanuj are in the ratio of 8 : 15. After 9 years, the ratio of their ages will be 11 : 18. What is the difference between their present ages?

  1. 21 years

  2. 28 years

  3. 35 years

  4. 22 years

  5. 12 years
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A Correct answer
Explanation

Let ages be 8x and 15x. (8x+9)/(15x+9) = 11/18. 18(8x+9) = 11(15x+9) => 144x + 162 = 165x + 99 => 21x = 63 => x = 3. Difference = 15x - 8x = 7x = 7 * 3 = 21.

AI explanation

Let the present ages of Samir and Tanuj be 8x and 15x years. After 9 years, the equation is 8x plus 9 divided by 15x plus 9 equals 11 divided by 18, which simplifies to 144x plus 162 equals 165x plus 99. Solving for x gives 21x equals 63, so x equals 3. The difference between their present ages is 15x minus 8x, which equals 7x, resulting in an age difference of 21 years.

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