Ratio and proportion

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

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

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

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.

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?

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.

Do you have enough information to work out the area of the shaded quadrilateral?

A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars. What combination of ingredients costing £5 per kg could he supply?