Multiple choice

The ratio of the present ages of a father and his son is 8 : 3. After 10 years, the ratio of their ages will be 2 : 1. Find the present age of the father.

  1. 40 years

  2. 45 years

  3. 50 years

  4. 55 years

  5. 60 years
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A Correct answer
Explanation

Let the father's age be 8x and the son's be 3x. After 10 years, the ratio is (8x+10)/(3x+10) = 2/1, which simplifies to 8x+10 = 6x+20, so 2x = 10 and x = 5. The father's present age is 8 * 5 = 40 years.

AI explanation

Let the present ages of the father and son be 8x and 3x. In 10 years, their ages will be 8x plus 10 and 3x plus 10, establishing the equation (8x plus 10) divided by (3x plus 10) equals 2. Solving this linear equation gives 8x plus 10 equals 6x plus 20, so 2x equals 10 and x equals 5. The present age of the father is 8 multiplied by 5, which is 40 years.

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