Multiple choice

Joseph said to his daughter Eva, "Seven years ago, I were seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." What is the present age of Eva?

  1. 12 years

  2. 15 years

  3. 14 years

  4. None of these

  5. 42 years
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A Correct answer
Explanation

Let J be Joseph's age and E be Eva's age. Seven years ago: J - 7 = 7(E - 7). Three years from now: J + 3 = 3(E + 3). Solving the first gives J = 7E - 42. Substituting into the second: 7E - 42 + 3 = 3E + 9, which simplifies to 4E = 48, so E = 12.

AI explanation

Let Joseph's and Eva's present ages be J and E respectively. Seven years ago, their ages were J - 7 and E - 7, giving the equation J - 7 = 7(E - 7). Three years from now, their ages will be J + 3 and E + 3, giving J + 3 = 3(E + 3). Expanding both equations yields J - 7E = -42 and J - 3E = 6, and subtracting the second from the first gives -4E = -48, so E = 12. Eva's present age is 12 years.

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