Multiple choice

The respective ratio of the present ages of a son and his father is 1 : 5 and that of his mother and father is 4 : 5. After two years, the respective ratio of the ages of the son and his mother will become 3 : 10. What is the present age of the father?

  1. 30 years

  2. 35 years

  3. 28 years

  4. 40 years

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

S:F = 1:5, M:F = 4:5. So S:M:F = 1:4:5. Let ages be x, 4x, 5x. After 2 years: (x+2)/(4x+2) = 3/10. 10x + 20 = 12x + 6, so 2x = 14, x = 7. Father's age = 5x = 35.

AI explanation

Let the present ages of the son, father, and mother be x, 5x, and 4x years respectively. The ratio equation for two years hence is (x + 2) divided by (4x + 2) equals 3 divided by 10. Cross-multiplying gives 10x + 20 = 12x + 6, so 2x = 14 and x = 7. The father's present age is 5 times 7, or 35 years.

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