Multiple choice

The ratio between the present ages of $M$ and $N$ is $5:3$ respectively The ratio between $M$'s age $4$ years ago and $N$'s age after $4$ years is $1:1$. What is the ratio between $M$'s age after $4$ years and $N$'s age $4$ years ago?

  1. $2:1$
  2. $1:3$
  3. $4:1$
  4. $3:1$
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D Correct answer
Explanation

Let the present ages be 5k and 3k. The condition 5k - 4 = 3k + 4 gives k = 4, so the present ages are 20 and 12. Their requested ages are 24 and 8, giving the ratio 24:8 = 3:1.

AI explanation

Let the present ages of M and N be 5x and 3x respectively. Since the ratio of M's age 4 years ago to N's age after 4 years is 1:1, we can write the equation (5x - 4) / (3x + 4) = 1 / 1. Solving this gives 5x - 4 = 3x + 4, which means 2x = 8 and x = 4. The required ratio of M's age after 4 years to N's age 4 years ago is (5x + 4) : (3x - 4), which substitutes to (20 + 4) : (12 - 4) = 24 : 8 = 3 : 1.

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