This is part of our collection of Short Problems.
You may also be interested in our longer problems on Ratio, Proportion and Rates of Change.
Printable worksheets containing selections of these problems are available here.
problem
Eating beans
Age
11 to 14
Challenge level
The Bean family are very particular about beans. At every meal all Beans eat some beans... At their last meal they ate 23 beans altogether. How many beans did Pa Bean eat?
problem
24 hour conundrum
Age
11 to 14
Challenge level
It is 225 minutes until midnight. What time is it on a 24-hour digital clock?
problem
Flying down under
Age
11 to 14
Challenge level
Fred flew to Melbourne, Australia. What time was it in Melbourne when Fred's flight arrived?
problem
Turbo tortoise
Age
11 to 14
Challenge level
Harriet Hare and Turbo Tortoise want to cross the finish line together on their 12 mile race.... What time should Harriet set off?
problem
Brothers and sisters
Age
11 to 14
Challenge level
Can you work out how many brothers and sisters are in the family?
problem
Minutes in between
Age
11 to 14
Challenge level
How many minutes are there between 11:41 and 14:02?
problem
Speed over a bridge
Age
11 to 14
Challenge level
How fast is the train travelling as it goes over the bridge?
problem
Flapjack
Age
11 to 14
Challenge level
A recipe for flapjacks calls for a certain quantity of butter, sugar and oats. Given the amount of these ingredients I have, how many flapjacks can I make?
problem
Roman distances
Age
11 to 14
Challenge level
Marcus' atrium was a square with each side 50 pedes long. How many times did Marcus have to walk round his atrium to complete his daily exercise of 8 stadia?
problem
Thunder and lightning
Age
11 to 14
Challenge level
How far away was the lightning if the flash and the thunderclap were 6 seconds apart?
problem
Race time
Age
11 to 14
Challenge level
Frank and Gabriel competed in a 200m race. Interpret the different units used for their times to work out who won.
problem
Dean's mountain
Age
11 to 14
Challenge level
Dean runs down the mountain at 12 km per hour. How long does it take him to run down the mountain?
problem
Three of a kind
Age
11 to 14
Challenge level
How long is it between 5:55 and the next time all three digits on a digital clock are the same?
problem
Printer ink
Age
11 to 14
Challenge level
A small ink cartridge has enough ink to print 600 pages. How many pages can be printed using a large ink cartridge?
problem
A classy ratio
Age
11 to 14
Challenge level
There are six more girls than boys in Miss Spelling's class of 24 pupils. What is the ratio of girls to boys in the class?
problem
Athletics club
Age
11 to 14
Challenge level
An athletics club has girl, boy and adult members. How many members does the club have?
problem
Draining a pool
Age
11 to 14
Challenge level
The water is being drained from a pool. After how long will the depth of the pool be 144 cm?
problem
Family fortune
Age
11 to 14
Challenge level
If three brothers will get £20 more if they do not share their money with their sister, how much money is there?
problem
Fruit basket ratio
Age
11 to 14
Challenge level
From two ratios of apples and oranges in a fruit bowl, can you work out how many fruits there are?
problem
Tyre wear
Age
11 to 14
Challenge level
A car with 5 tyres (four road tyres and a spare) travelled 30,000 km. All 5 tyres were used equally. How many kilometres' wear did each tyre receive?
problem
Leg it
Age
11 to 14
Challenge level
How far from the finishing line should these runners start to make the race 'fair'?
problem
Musical maths
Age
11 to 14
Challenge level
Approximately how long is five hundred and twenty five thousand six hundred minutes?
problem
Don't be late
Age
11 to 14
Challenge level
Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.
problem
Off the cuff
Age
11 to 14
Challenge level
Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?
problem
A leg to stand on
Age
11 to 14
Challenge level
Can you work out the number of chairs at a cafe from the number of legs?
problem
Out of sync
Age
11 to 14
Challenge level
Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?
problem
Ratio swap
Age
11 to 14
Challenge level
How many adults would need to join this group of people to reverse this ratio?
problem
Decimal clock
Age
11 to 14
Challenge level
A decimal clock is started at midnight. What time would it show at 6 o'clock in the morning?
problem
Sharing sweets
Age
11 to 14
Challenge level
Maria and Lucy spun a coin 30 times, and gave each other sweets depending on the outcome of the spin. How many times was tails spun?
problem
How many swimmers?
Age
11 to 14
Challenge level
Given the ratios of junior to senior and senior to veteran members, can you work out what the smallest possible number of members in a swimming club is?
problem
Stair climb
Age
11 to 14
Challenge level
Three people run up stairs at different rates. If they each start from a different point - who will win, come second and come last?
problem
The elephant diet
Age
11 to 14
Challenge level
Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day
problem
Washing elephants
Age
11 to 14
Challenge level
How long will it take Mary and Nigel to wash an elephant if they work together?
problem
Revolutions
Age
11 to 14
Challenge level
Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?
problem
Honey bees
Age
14 to 16
Challenge level
How many bees could fly 1000 miles if they had 10 gallons of honey?
problem
Tummy ache
Age
14 to 16
Challenge level
Timmy, Tammy and Tommy all go to the doctors. In what order do they arrive at the surgery?
problem
Hiking the hill
Age
14 to 16
Challenge level
Sarah's average speed for a journey was 2 mph, and her return average speed was 4 mph. What is her average speed for the whole journey?
problem
The London Eye
Age
14 to 16
Challenge level
The 80 spokes of The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?
problem
Caught in the web
Age
14 to 16
Challenge level
Can you estimate the mass of insects caught by spiders in the UK each year?
problem
Platinum puzzle
Age
14 to 16
Challenge level
What is the approximate total volume of platinum that has ever been produced?
problem
Pond runners
Age
14 to 16
Challenge level
Can you work out how much time it will be before Katherine laps James around the pond?
problem
Walking in the mountains
Age
14 to 16
Challenge level
Heidi and Peter pass two signs which say how far their destination is. How long will it take them to get there?
problem
Inches and barleycorns
Age
14 to 16
Challenge level
How many barleycorns are there in one inch?
problem
Shepherd's flock
Age
14 to 16
Challenge level
Does Joseph have too many sheep in his flock...
problem
Overtake
Age
14 to 16
Challenge level
Tom and Tim are travelling towards Glasgow, but leave at different times. If Tim overtakes Tom, how fast is he travelling?
problem
Bike shop
Age
14 to 16
Challenge level
If I walk to the bike shop, but then cycle back, what is my average speed?
problem
Travelling by train
Age
14 to 16
Challenge level
Stephen stops at Darlington on his way to Durham. At what time does he arrive at Durham?
problem
Hillwalking
Age
14 to 16
Challenge level
Andrew walks along a flat path, then up and down a hill, then back along the path. Is it possible to work out how far he has walked?
problem
Very long line
Age
14 to 16
Challenge level
If the line on the right were 0.2mm thick, how long would it need to be to cover an area of one square metre?
problem
Travelator
Age
14 to 16
Challenge level
When Andrew arrives at the end of the walkway, how far is he ahead of Bill?
problem
Dolly dolphin
Age
14 to 16
Challenge level
Can you find Dolly Dolphin's average speed as she swims with and against the current?
problem
Ratio riddle
Age
14 to 16
Challenge level
Can you work out the ratio b:c given the ratios a:b and a:c?
problem
Tyneside average speed
Age
14 to 16
Challenge level
Can you work out the average speed of the van?
problem
Crude calculation
Age
14 to 16
Challenge level
Louise has noticed that the price of petrol has changed. Can you work out the percentage that it has increased by?
problem
Antifreeze
Age
14 to 16
Challenge level
How much more antifreeze is needed to make the proportion 30%?
problem
Day out
Age
14 to 16
Challenge level
Chris cycled faster than expected. Can you work out his average speed?
problem
Boys and girls
Age
14 to 16
Challenge level
Can you find the total number of students in the school, given some information about ratios?
problem
Laps
Age
14 to 16
Challenge level
On which of the hare's laps will she first pass the tortoise?
problem
Backwards laps
Age
14 to 16
Challenge level
If two friends run in opposite directions around a track, and they pass each other every 24 seconds, how long do they take to complete a lap?
problem
Petrol stop
Age
14 to 16
Challenge level
From the information given, can you work out how long Roberto drove for after putting petrol in his car?
problem
Televisual technology
Age
14 to 16
Challenge level
If a new and an old television have screens of the same area, what is the ratio of their widths?
problem
Traffic jam
Age
14 to 16
Challenge level
Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced?
problem
Marathon mission
Age
14 to 16
Challenge level
Minnie trained more for the London Marathon this year, so her speed increased. By what percentage did her time decrease?
problem
Flower show
Age
14 to 16
Challenge level
How long will it take six gardeners to dig six circular flower beds?
problem
Late for work
Age
14 to 16
Challenge level
What average speed should Ms Fanthorpe drive at to arrive at work on time?
problem
Walk up the escalator
Age
14 to 16
Challenge level
Can you work out how long Aimee would take to get up the escalator if she walked?
problem
Two trains
Age
14 to 16
Challenge level
Two trains started simultaneously, each travelling towards the other. How long did each train need to complete the journey?
problem
100m sprint
Age
14 to 16
Challenge level
Anna, Bridget and Carol run a race. Can you work out where Carol was when Anna finished?