Now I am 40 years old.
I tell you:
“I am 4 times the age you were when I was the age you are now.”
How old are you currently?
Home > Riddles > The ages in a temporal mirror
The ages in a temporal mirror
Hints
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- Quick check: I am now 40, which is 4 times 10.
- Resolving: $10=2x-40 \Rightarrow 2x=50 \Rightarrow x=25$.
- Quick check: If you're 25 now, 15 years ago you were 10.
Solution
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Answer: You are 25 years old.
Method:
Let $x$ be your current age. I am 40.
When I was your current age ($x$), that was $(40-x)$ years ago.
At that time, you had:
$$ x-(40-x)=2x-40. $$
The statement says that my current age (40) is 4 times that age:
$$ 40=4(2x-40). $$
Solving:
$$ 10=2x-40 \Rightarrow 2x=50 \Rightarrow x=25. $$
Quick Check:
- If you are 25 now, 15 years ago you were 10.
- I am now 40, which is 4 times 10.
Correct.
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