Multiple choice

The ages of $A$ and $B$ are in the ratio $3 : 1$. Fifteen years hence, the ratio will be $2 : 1$. Their present ages, respectively, are

  1. $30$ years, $10$ years
  2. $45$ years, $15$ years
  3. $21$ years, $7$ years
  4. $60$ years, $20$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the ages be 3x and x. After 15 years, (3x+15)/(x+15) = 2/1. Solving gives 3x + 15 = 2x + 30, so x = 15. The ages are 3(15) = 45 and 15.

AI explanation

Let the present ages of A and B be 3x and x. Using the ratio method, after fifteen years their ages will be 3x + 15 and x + 15, giving the equation (3x + 15) / (x + 15) = 2 / 1. Cross multiplying gives 3x + 15 = 2x + 30, which simplifies to x = 15. The present ages are 3 * 15 = 45 years for A and 15 years for B.

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