Exercise 50

In 1936, John said to Bob, "You are twice my age". If both were alive by the year 2000 and their ages added up to 140 years, how old was John in 2000?

  1. 68

  2. 80

  3. 74

  4. 72

  5. 76

Try to solve it before checking the answer.

  1. 68

Between 1936 to 2000 there were:

\[ 2000 – 1936 = 64 \; \text{years} \]

If \(x\) was the age of Jhon by the year 2000, then:

  • The age of Bob by 2000 was:   \( 140 – x \)

  • The age of Jhon by 1936 was:   \( x – 64 \)

  • The age of Bob by 1936 was:

    \[ 140 – x – 64 = 76 – x \]

Since the age of Bob by the year 1936 was the double of Jhon’s, we have:

\[ \begin{aligned} &76 – x = 2 (x – 64) \\[.5em] &\hspace{6em} \Rightarrow 76 – x = 2x – 128 \\[.5em] &\hspace{6em} \Rightarrow 3x = 204 \\[.5em] &\hspace{6em} \Rightarrow x = \boldsymbol{68} \end{aligned} \]
\[ \begin{aligned} 76 – x = 2 (x – 64) &\Rightarrow 76 – x = 2x – 128 \\[.5em] &\Rightarrow 3x = 204 \\[.5em] &\Rightarrow x = \boldsymbol{68} \end{aligned} \]

Hence, by the year 2000 Jhon was 68 years old.

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