### Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) is the width decreased by ?

### Circle Packing

Equal circles can be arranged so that each circle touches four or six others. What percentage of the plane is covered by circles in each packing pattern? ...

### Round and Round

Prove that the shaded area of the semicircle is equal to the area of the inner circle.

##### Stage: 4 Short Challenge Level:

On the television programme Antiques Roadshow, a painting was said to be worth £15 000 although the painting originally cost only 50p. As a percentage of the original price, what would be the approximate profit if the painting were to be sold for £15 000?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
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