A short statement can hide more than it seems. Here a careless reading is enough to arrive at the wrong answer; A careful reading, on the other hand, resolves it effortlessly.
The ages in a temporal mirror
Riddle statement
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?
Show solution
Solution
Answer: You are 25 years old.
Let \(x\) be your current age. When I was your age, I was \(40 - x\) years away from reaching the present, so you were then:
$x - (40 - x) = 2x - 40.$
The statement states that my current age, 40, is four times that quantity:
$40 = 4(2x - 40).$
Solving:
$40 = 8x - 160,$
$8x = 200,$
$x = 25.$
Your current age is 25 years.