Multiple choice

The present ages of $A$ and $B$ are in the ratio $15:8$. After ten years, their ages will be in the ratio $5:3$. Find their present ages.

  1. $A= 60$ years and $B= 32$ years
  2. $A= 20$ years and $B= 32$ years
  3. $A= 70$ years and $B= 42$ years
  4. $A= 30$ years and $B= 12$ years
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A Correct answer
Explanation

Let the ages be 15x and 8x. After 10 years, (15x + 10)/(8x + 10) = 5/3. Cross-multiplying gives 45x + 30 = 40x + 50, so 5x = 20 and x = 4. The ages are 15 * 4 = 60 and 8 * 4 = 32.

AI explanation

Let the present ages of A and B be $15x$ and $8x$ respectively. After 10 years, the ratio of their ages will be 5:3, giving the equation $(15x + 10) / (8x + 10) = 5 / 3$. Cross-multiplying yields $3(15x + 10) = 5(8x + 10)$, which simplifies to $45x + 30 = 40x + 50$. Solving for $x$ gives $5x = 20$, so $x = 4$. Multiplying the initial ratio values by 4 means A is $15 \times 4 = 60$ years old and B is $8 \times 4 = 32$ years old.

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