Multiple choice

The ages of A and B are in the ratio $5:3$. After $6$ years, their ages will be in the ratio $7:5$. The sum of their present ages is __________.

  1. $9$ years
  2. $10$ years
  3. $15$ years
  4. $24$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let ages be 5x and 3x. (5x+6)/(3x+6) = 7/5. 25x + 30 = 21x + 42. 4x = 12, x = 3. Present ages are 15 and 9. Sum = 24.

AI explanation

Let the present ages of A and B be 5x and 3x respectively. After 6 years, their ages will be 5x plus 6 and 3x plus 6, giving the proportion 5x plus 6 divided by 3x plus 6 equals 7 divided by 5. Solving the equation 5 times (5x plus 6) equals 7 times (3x plus 6) yields 25x plus 30 equals 21x plus 42, meaning x equals 3. The sum of their present ages is 5x plus 3x, which is 8 times 3, or 24 years.