Ratio and proportion

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Favourite

Rule of Three

Age

11 to 14

Challenge level

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
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All About Ratios

Age

16 to 18

Challenge level

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

Age

14 to 16

Challenge level

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?
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Equal Temperament

Age

14 to 16

Challenge level

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.
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Little Man

Age

5 to 7

Challenge level

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?
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Blackcurrantiest

Age

5 to 7

Challenge level

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

Age

7 to 11

Challenge level

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?
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Orange Drink

Age

7 to 11

Challenge level

A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink?
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Number Lines in Disguise

Age

7 to 14

Challenge level

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

Cereal Mix

Age

11 to 14

Challenge level

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?