Exercise 28

A father says to his son, “Now your age is a third of mine, but 10 years ago it was only a fifth.” In 5 years the son will be:

  1. 18 years old

  2. 25 years old

  3. 21 years old

  4. 29 years old

  5. 20 years old

Try to solve it before checking the answer.

  1. 25 years old

If \(x \) is the age of the son, we have:

  • Current father’s age:   \(3x\)

  • Age of the son 10 years ago:   \( x – 10 \)

  • Age of the father 10 years ago:   \( 3x – 10 \)

As the age of the father 10 years ago was 5 times that of the son, we have:

\[ \begin{aligned} &3x – 10 = 5 (x – 10) \\[.5em] &\hspace{4em} \Rightarrow 3x – 10 = 5x – 50 \\[.5em] &\hspace{4em}\Rightarrow 2x = 40 \\[.5em] &\hspace{4em}\Rightarrow x = 20 \end{aligned} \]
\[ \begin{aligned} 3x – 10 = 5 (x – 10) &\Rightarrow 3x – 10 = 5x – 50 \\[.5em] &\Rightarrow 2x = 40 \\[.5em] &\Rightarrow x = 20 \end{aligned} \]

The current age of the son is 20. Hence, in 5 years he will be 25 years old.

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