This riddle looks so easy that it almost invites you to answer without thinking. But the important phrase is not the total price; it is the difference between the two items.
The Bottle and the Cap
Riddle statement
A bottle and its cap cost €1.10 in total.
The bottle costs exactly €1 more than the cap.
How much does the cap cost?
Show solution
Solution
The impulsive answer is usually 10 cents, but that cannot be right.
If the cap cost €0.10, then the bottle would cost €1 more:
$
1.10\ €
$
Together they would cost:
$
1.10 + 0.10 = 1.20\ €
$
But the total must be €1.10.
Let $x$ be the price of the cap.
Then the bottle costs:
$
x+1
$
Together they cost:
$
x+(x+1)=1.10
$
Therefore:
$
2x+1=1.10
$
$
2x=0.10
$
$
x=0.05
$
The cap costs 5 cents, and the bottle costs €1.05.
Answer: the cap costs 5 cents.