Multiple choice

A girl is twice as old as her sister. Four years hence, the product of their ages (in years) will be $160$. Find the present age of her sister.

  1. $12$ yrs
  2. $6$ yrs
  3. $8$ yrs
  4. $9$ yrs
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let sister's age be x, girl's age be 2x. Four years later, (x+4)(2x+4) = 160. 2x^2 + 12x + 16 = 160, so 2x^2 + 12x - 144 = 0, or x^2 + 6x - 72 = 0. Solving (x+12)(x-6) = 0, we get x=6.

AI explanation

Let the sister's present age be S, so the girl's age is 2S. Four years hence, their ages will be S + 4 and 2S + 4, and their product is 160. The equation is (S + 4)(2S + 4) = 160, which simplifies to 2S^2 + 12S minus 144 = 0. Solving this quadratic equation yields S = 6. The sister's present age is 6 years.

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