Ratio and proportion

  • A stone obelisk on a grassy hill.
    problem

    Zin Obelisk

    Age
    11 to 14
    Challenge level
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    In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.

  • Tyre Wear
    problem

    Tyre Wear

    Age
    11 to 14
    Challenge level
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    A car with 5 tyres (four road tyres and a spare) travelled 30,000 km. All 5 tyres were used equally. How many kilometres' wear did each tyre receive?

  • Place value, integers, ordering and rounding - Short Problems
    problem

    Washing Elephants

    Age
    11 to 14
    Challenge level
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    How long will it take Mary and Nigel to wash an elephant if they work together?

  • Square Pegs
    problem

    Square Pegs

    Age
    11 to 14
    Challenge level
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    Which is a better fit, a square peg in a round hole or a round peg in a square hole?

  • Do unto Caesar
    problem

    Do Unto Caesar

    Age
    11 to 14
    Challenge level
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    At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?

  • Hello Again
    problem

    Hello Again

    Age
    11 to 14
    Challenge level
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    Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

  • Hexagon Slices
    problem

    Hexagon Slices

    Age
    11 to 14
    Challenge level
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    Weekly Problem 37 - 2007
    This regular hexagon has been divided into four trapezia and one hexagon.... what is the ratio of the lengths of sides p, q and r?

  • Ratio Sudoku 2
    problem

    Ratio Sudoku 2

    Age
    11 to 16
    Challenge level
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    A Sudoku with clues as ratios.

  • Ratio Sudoku 3
    problem

    Ratio Sudoku 3

    Age
    11 to 16
    Challenge level
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    A Sudoku with clues as ratios or fractions.

  • Star Gazing
    problem

    Star Gazing

    Age
    14 to 16
    Challenge level
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    Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.