Ratio and proportion

problem

Meeting Point

Age

14 to 16

Challenge level

1 out of 3

Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?
problem

Tennis Club

Age

14 to 16

Challenge level

1 out of 3

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?
problem

Contact

Age

14 to 16

Challenge level

2 out of 3

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
problem

Gift of Gems

Age

14 to 16

Challenge level

2 out of 3

Four jewellers share their stock. Can you work out the relative values of their gems?
problem

Burning Down

Age

14 to 16

Challenge level

2 out of 3

One night two candles were lit. Can you work out how long each candle was originally?
problem

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?
problem

Rhombus in Rectangle

Age

14 to 16

Challenge level

2 out of 3

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.
problem

Tin Tight

Age

14 to 16

Challenge level

2 out of 3

What's the most efficient proportion for a 1 litre tin of paint?
problem

Square Ratio

Age

14 to 16

Challenge level

2 out of 3

A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?
problem

Pythagoras' Comma

Age

14 to 16

Challenge level

2 out of 3

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.