Multiple choice

If Dennis is $\left (\displaystyle \frac{1}{3}\right)^{rd}$ the age of his father Keith now and was $\left (\displaystyle \frac{1}{4}\right)^{th}$ the age of his father $5$ years age then how old will his father Keith be $5$ years from now?

  1. $20$ years
  2. $45$ years
  3. $40$ years
  4. $50$ years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Keith's present age be F, so Dennis is F/3. Five years ago, the relation was F/3 - 5 = (F - 5)/4, which gives F = 45; therefore, Keith will be 50 in five years.

AI explanation

Let Dennis's present age be d and his father Keith's present age be k. We are given d = k / 3. Five years ago, their ages were d - 5 and k - 5, so d - 5 = (k - 5) / 4. Multiplying the first equation by 3 gives 3d = k, and multiplying the second equation by 4 gives 4d - 20 = k - 5. Substituting k gives 4d - 20 = 3d - 5, meaning d = 15. Keith's present age is 3 * 15 = 45 years. Five years from now, Keith will be 45 + 5 = 50 years.

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