Multiple choice

A woman is 30 years older than her son. Fifteen years ago, she was twice as old as her son. Find their present ages.

  1. Age of woman = 75 years, Age of son = 35 years

  2. Age of woman = 45 years, Age of son = 25 years

  3. Age of woman = 85 years, Age of son = 35 years

  4. Age of woman = 75 years, Age of son = 45 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let son's age be x, woman's age be x + 30. 15 years ago: (x + 30 - 15) = 2 * (x - 15). x + 15 = 2x - 30. x = 45. Woman is 45 + 30 = 75. Option D matches these values.

AI explanation

Let the present ages of the woman and her son be W and S. The first condition gives W = S + 30. Fifteen years ago, the equation W minus 15 = 2(S minus 15) simplifies to W = 2S minus 15. Equating the two expressions for W gives S + 30 = 2S minus 15, which yields S = 45. Substituting S = 45 into the first equation gives W = 45 + 30 = 75.

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