The Bat and Ball Puzzle
A bat and a ball cost £1.10. The bat costs £1.00.How much does the ball cost?
Many people will say 10 pence (or £0.10).
THIS IS WRONG!
If the ball did cost cos £0.10 then the bat =would cost £0.90 more, as opposed to the £1.00 more given in the question.
Suppose the ball costs £
\[x\]
.Then the bat cost £
\[1+x\]
.Then
\[(1+x)+x=1.10\]
\[1+2x=1.10 \rightarrow x=\frac{1.1-1}{2}=0.05\]
The ball costs
\[£0.05\]
and the bat costs £1.05.