Ratio and proportion

  • Temperature
    problem
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    Temperature

    Age
    11 to 14
    Challenge level
    2 out of 3

    Is there a temperature at which Celsius and Fahrenheit readings are the same?

  • Triathlon and Fitness
    problem
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    Triathlon and Fitness

    Age
    11 to 14
    Challenge level
    2 out of 3

    The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

  • Oh for the mathematics of yesteryear
    problem
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    Oh for the Mathematics of Yesteryear

    Age
    11 to 14
    Challenge level
    3 out of 3

    A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy?

  • A Chance to Win?
    problem
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    A Chance to Win?

    Age
    11 to 14
    Challenge level
    3 out of 3

    Imagine you were given the chance to win some money... and imagine you had nothing to lose...

  • Ratio Sudoku 1
    problem
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    Ratio Sudoku 1

    Age
    11 to 16
    Challenge level
    2 out of 3

    A Sudoku with clues as ratios.

  • Nutrition and Cycling
    problem
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    Nutrition and Cycling

    Age
    14 to 16
    Challenge level
    1 out of 3

    Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

  • Two Ladders
    problem
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    Two Ladders

    Age
    14 to 16
    Challenge level
    2 out of 3

    Two ladders are propped up against facing walls. At what height do the ladders cross?

  • One and three
    problem
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    One and Three

    Age
    14 to 16
    Challenge level
    2 out of 3

    Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400 metres from B. How long is the lake?

  • Sitting Pretty
    problem
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    Sitting Pretty

    Age
    14 to 16
    Challenge level
    2 out of 3

    A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?