Multiple choice

The present age of a man is 3 times that of his son Six years ago the age of the man was four times that of his son. Find the ratio of their ages 6 years later.

  1. $4 : 3$
  2. $3 : 4$
  3. $2 : 5$
  4. $5 : 2$
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D Correct answer
Explanation

Let son's age be x, man's age be 3x. Six years ago: 3x-6 = 4(x-6). 3x-6 = 4x-24. x = 18. Present ages: son 18, man 54. Six years later: son 24, man 60. Ratio = 60:24 = 5:2.

AI explanation

Let the present ages of the son and the man be x and 3x respectively. Six years ago, their ages were x minus 6 and 3x minus 6, yielding the equation 3x minus 6 equals 4 times (x minus 6). Solving this gives 3x minus 6 equals 4x minus 24, so x equals 18, meaning the current ages are 18 and 54. Six years later, their ages will be 24 and 60, giving a ratio of 5 to 2.

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