Ratio and proportion

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?

A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.

Can you work out how to produce different shades of pink paint?

Can you find an efficent way to mix paints in any ratio?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Build a scaffold out of drinking-straws to support a cup of water