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 ?

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.

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?

Weekly Problem 47 - 2007

Stage: 3 and 4 Challenge Level:

$2007\%$ 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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