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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 ?

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Mathland Election

A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.

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One or Both

Problem one was solved by 70% of the pupils. Problem 2 was solved by 60% of them. Every pupil solved at least one of the problems. Nine pupils solved both problems. How many pupils took the exam?

Percentage Swap

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

$2007\%$ of $50$ is $2007\times50/100$, which is the same as $50\times2007/100$, or $50\%$ of $2007$. Hence the answer is $100\%$ of $2007$, which is $2007$.

This problem is taken from the UKMT Mathematical Challenges.
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