Ratio and proportion

  • At a glance
    problem

    At a Glance

    Age
    14 to 16
    Challenge level
    The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
  • Around and Back
    problem

    Around and Back

    Age
    14 to 16
    Challenge level
    A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns around and heads back to the starting point where he meets the runner who is just finishing his first circuit. Find the ratio of their speeds.
  • Semi-Square
    problem

    Semi-Square

    Age
    14 to 16
    Challenge level
    What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
  • Rati-o
    problem

    Rati-O

    Age
    11 to 14
    Challenge level
    Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
  • Bus Stop
    problem

    Bus Stop

    Age
    14 to 16
    Challenge level
    Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant and in the ratio 5 to 4. The buses travel to and fro between the towns. What milestones are at Shipton and Veston?
  • Half a Triangle
    problem

    Half a Triangle

    Age
    14 to 16
    Challenge level
    Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.
  • Exact dilutions
    problem

    Exact Dilutions

    Age
    14 to 16
    Challenge level
    Which exact dilution ratios can you make using only 2 dilutions?
  • Scale Draw
    problem

    Scale Draw

    Age
    5 to 7
    Challenge level

    Use the grids to draw pictures to different scales.

  • Blackcurrantiest
    problem

    Blackcurrantiest

    Age
    5 to 7
    Challenge level

    Can you decide whose drink has the strongest blackcurrant flavour from these pictures?

  • Cherry Buns
    problem

    Cherry Buns

    Age
    7 to 11
    Challenge level

    Sam's grandmother has an old recipe for cherry buns. She has enough mixture to put 45 grams in each of 12 paper cake cases. What was the weight of one egg?

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