Multiple choice

The ratio of the ages of a father and his son at present is 5 : 2. After four years, the ratio of the ages of the son and his mother will be 1 : 2. What is the ratio of the present age of the father to that of the mother?

  1. 3 : 4

  2. 5 : 4

  3. 4 : 3

  4. Cannot be determined

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

Let Father = 5x, Son = 2x. After 4 years, Son = 2x+4. The ratio of Son to Mother is 1:2, so Mother = 2(2x+4) = 4x+8. The ratio of Father to Mother is 5x/(4x+8), which depends on x; therefore, it cannot be determined.

AI explanation

Let the present ages of the father, son, and mother be F, S, and M. The ratio of father to son is 5 to 2, so F = 5x and S = 2x. After four years, the ratio of son to mother is 1 to 2, meaning (2x + 4) / (M + 4) = 1 / 2, which simplifies to M = 4x + 4. The ratio of father to mother would be 5x / (4x + 4), which depends on the unknown value of x. Since there is no second equation to find x, the ratio cannot be determined.

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