### Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage 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.

# Dating Made Easier

##### Age 14 to 16Challenge Level

If a sum invested gains $10\%$ each year how long will it be before it has doubled its value?

If an object depreciates in value by $10\%$ each year how long will it take until only half of the original value remains?

Why aren't these two answers the same?

Is there a rate, used for both gain and depreciation, for which those two answers would actually be the same? How do you know?

If this problem caught your interest and you know some Stage 5 mathematics, this Plus article on Carbon Dating could be a good next step for you.