Someone says:
"Now I am 40 years old, and today I am 4 times the age you were when I was the age you are now."
How old are you now?
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The ages in a temporal mirror
The ages in time mirror is brief, but not small: it works because an automatic assumption is enough to ruin it. Its best reading is to take the statement literally and not add anything more.
Hints
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- Call x your current age and literally translate each phrase in the statement.
- When I was your age, that happened 40 - x years ago.
- The age you were then is also expressed in terms of x; then impose the relationship 'four times'.
Solution
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Answer: You are 25 years old. Explanation: Let $x$ be your current age. When I was your current age, they had passed
$$ 40-x $$
years from then to today. At that time, your age was
$$ x-(40-x)=2x-40. $$ The statement says that my current age, 40, is four times that age: $$
40=4(2x-40).
$$ Solving:
$$ 40=8x-160,\qquad 8x=200,\qquad x=25. $$ So your current age is **25 years old**. $$
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