Ratio and proportion

  • Racing odds
    problem

    Racing Odds

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?
  • Conical Bottle
    problem

    Conical Bottle

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?
  • Circuit training
    problem

    Circuit Training

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?
  • Tuning and Ratio
    problem

    Tuning and Ratio

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?
  • Punky Fish
    problem

    Punky Fish

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?
  • Meeting Point
    problem

    Meeting Point

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?
  • Eudiometry
    problem

    Eudiometry

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    When a mixture of gases burn, will the volume change?
  • Diamonds aren't forever
    problem

    Diamonds Aren't Forever

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    Ever wondered what it would be like to vaporise a diamond? Find out inside...
  • Tennis Club
    problem

    Tennis Club

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?