## The Bat and Ball Puzzle

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.