Multiple choice

Aftab tells his daughter, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." (Isn't this interesting?) What are their present ages?

  1. $12, 42$
  2. $13, 47$
  3. $18, 51$

  4. None of these
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A Correct answer
Explanation

Let A be Aftab's age and D be daughter's age. (A-7) = 7(D-7) => A-7 = 7D-49 => A = 7D-42. (A+3) = 3(D+3) => A+3 = 3D+9 => A = 3D+6. Equating: 7D-42 = 3D+6 => 4D = 48 => D = 12. Then A = 3(12)+6 = 42.

AI explanation

Let Aftab's present age be x years and his daughter's age be y years. From the first condition, x - 7 = 7 times (y - 7), which simplifies to x = 7y - 42. From the second condition, x + 3 = 3 times (y + 3), which simplifies to x = 3y + 6. Equating the expressions gives 7y - 42 = 3y + 6, so 4y = 48 and y = 12. Substituting y into the second equation gives x = 42, making their present ages 42 and 12.

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