Ratio, Proportion and Rates of Change - Short Problems


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.

Three of a Kind

Age 11 to 14 Short Challenge Level:

How long is it between 5:55 and the next time all three digits on a digital clock are the same?

Printer Ink

Age 11 to 14 Short Challenge Level:

A small ink cartridge has enough ink to print 600 pages. How many pages can be printed using a large ink cartridge?

Flying Down Under

Age 11 to 14 Short Challenge Level:

Fred flew to Melbourne, Australia. What time was it in Melbourne when Fred's flight arrived?

A Classy Ratio

Age 11 to 14 Short 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?

Turbo Tortoise

Age 11 to 14 Short 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?

Brothers and Sisters

Age 11 to 14 Short Challenge Level:

Can you work out how many brothers and sisters are in the family?

Dean's Mountain

Age 11 to 14 Short Challenge Level:

Dean runs down the mountain at 12 km per hour. How long does it take him to run down the mountain?

Draining a Pool

Age 11 to 14 Short Challenge Level:

The water is being drained from a pool. After how long will the depth of the pool be 144 cm?

Race Time

Age 11 to 14 Short Challenge Level:

Frank and Gabriel competed in a 200m race. Interpret the different units used for their times to work out who won.

Athletics Club

Age 11 to 14 Short Challenge Level:

An athletics club has girl, boy and adult members. How many members does the club have?

Minutes in Between

Age 11 to 14 Short Challenge Level:

How many minutes are there between 11:41 and 14:02?

Speed over a Bridge

Age 11 to 14 Short Challenge Level:

How fast is the train travelling as it goes over the bridge?

Family Fortune

Age 11 to 14 Short Challenge Level:

If three brothers will get £20 more if they do not share their money with their sister, how much money is there?

Flapjack

Age 11 to 14 Short 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?

Eating Beans

Age 11 to 14 Short 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?

24 Hour Conundrum

Age 11 to 14 Short Challenge Level:

It is 225 minutes until midnight. What time is it on a 24-hour digital clock?

Roman Distances

Age 11 to 14 Short 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?

Thunder and Lightning

Age 11 to 14 Short Challenge Level:

How far away was the lightning if the flash and the thunderclap were 6 seconds apart?

Millennium Leap

Age 11 to 14 Short Challenge Level:

How many leap years will there be between 2001 and 3001?

Decimal Clock

Age 11 to 14 Short Challenge Level:

A decimal clock is started at midnight. What time would it show at 6 o'clock in the morning?

Off the Cuff

Age 11 to 14 Short Challenge Level:

Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?

Musical Maths

Age 11 to 14 Short Challenge Level:

Approximately how long is five hundred and twenty five thousand six hundred minutes?

The Elephant Diet

Age 11 to 14 Short Challenge Level:

Use the relationship between the elephant and the rabbit to find out how many carrots the rabbit eats in a day

Don't Be Late

Age 11 to 14 Short Challenge Level:

Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

Ratio Swap

Age 11 to 14 Short Challenge Level:

How many adults would need to join this group of people to reverse this ratio?

Sharing Sweets

Age 11 to 14 Short 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?

Tyre Wear

Age 11 to 14 Short 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?

A Leg to Stand On

Age 11 to 14 Short Challenge Level:

Can you work out the number of chairs at a cafe from the number of legs?

Fruit Basket Ratio

Age 11 to 14 Short Challenge Level:

From two ratios of apples and oranges in a fruit bowl, can you work out how many fruits there are?

How Many Swimmers?

Age 11 to 14 Short 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?

Leg It

Age 11 to 14 Short Challenge Level:

How far from the finishing line should these runners start to make the race 'fair'?

Out of Sync

Age 11 to 14 Short 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?

Stair Climb

Age 11 to 14 Short 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?

Revolutions

Age 11 to 14 Short 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?

Washing Elephants

Age 11 to 14 Short Challenge Level:

How long will it take Mary and Nigel to wash an elephant if they work together?

The London Eye

Age 14 to 16 Short Challenge Level:

The 80 spokes of The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?

Caught in the Web

Age 14 to 16 Short Challenge Level:

Can you estimate the mass of insects caught by spiders in the UK each year?

Honey Bees

Age 14 to 16 Short Challenge Level:

How many bees could fly 1000 miles if they had 10 gallons of honey?

Tummy Ache

Age 14 to 16 Short Challenge Level:

Timmy, Tammy and Tommy all go to the doctors. In what order do they arrive at the surgery?

Hiking the Hill

Age 14 to 16 Short 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?

Crude Calculation

Age 14 to 16 Short Challenge Level:

Louise has noticed that the price of petrol has changed. Can you work out the percentage that it has increased by?

Walking in the Mountains

Age 14 to 16 Short Challenge Level:

Heidi and Peter pass two signs which say how far their destination is. How long will it take them to get there?

Antifreeze

Age 14 to 16 Short Challenge Level:

How much more antifreeze is needed to make the proportion 30%?

Inches and Barleycorns

Age 14 to 16 Short Challenge Level:

How many barleycorns are there in one inch?

Travelling by Train

Age 14 to 16 Short Challenge Level:

Stephen stops at Darlington on his way to Durham. At what time does he arrive at Durham?

Shepherd's Flock

Age 14 to 16 Short Challenge Level:

Does Joseph have too many sheep in his flock...

Travelator

Age 14 to 16 Short Challenge Level:

When Andrew arrives at the end of the walkway, how far is he ahead of Bill?

Hillwalking

Age 14 to 16 Short 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?

Ratio Riddle

Age 14 to 16 Short Challenge Level:

Can you work out the ratio b:c given the ratios a:b and a:c?

Very Long Line

Age 14 to 16 Short 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?

Overtake

Age 14 to 16 Short Challenge Level:

Tom and Tim are travelling towards Glasgow, but leave at different times. If Tim overtakes Tom, how fast is he travelling?

Tyneside Average Speed

Age 14 to 16 Short Challenge Level:

Can you work out the average speed of the van?

Platinum Puzzle

Age 14 to 16 Short Challenge Level:

What is the approximate total volume of platinum that has ever been produced?

Pond Runners

Age 14 to 16 Short Challenge Level:

Can you work out how much time it will be before Katherine laps James around the pond?

Bike Shop

Age 14 to 16 Short Challenge Level:

If I walk to the bike shop, but then cycle back, what is my average speed?

Dolly Dolphin

Age 14 to 16 Short Challenge Level:

Can you find Dolly Dolphin's average speed as she swims with and against the current?

Day Out

Age 14 to 16 Short Challenge Level:

Chris cycled faster than expected. Can you work out his average speed?

Candles

Age 14 to 16 Short Challenge Level:

What is the ratio of the lengths of the candles?

Petrol Stop

Age 14 to 16 Short Challenge Level:

From the information given, can you work out how long Roberto drove for after putting petrol in his car?

Marathon Mission

Age 14 to 16 Short Challenge Level:

Minnie trained more for the London Marathon this year, so her speed increased. By what percentage did her time decrease?

Walk up the Escalator

Age 14 to 16 Short Challenge Level:

Can you work out how long Aimee would take to get up the escalator if she walked?

100m Sprint

Age 14 to 16 Short Challenge Level:

Anna, Bridget and Carol run a race. Can you work out where Carol was when Anna finished?

Flower Show

Age 14 to 16 Short Challenge Level:

How long will it take six gardeners to dig six circular flower beds?

Boys and Girls

Age 14 to 16 Short Challenge Level:

Can you find the total number of students in the school, given some information about ratios?

Televisual Technology

Age 14 to 16 Short Challenge Level:

If a new and an old television have screens of the same area, what is the ratio of their widths?

Laps

Age 14 to 16 Short Challenge Level:

On which of the hare's laps will she first pass the tortoise?

Two Trains

Age 14 to 16 Short Challenge Level:

Two trains started simultaneously, each travelling towards the other. How long did each train need to complete the journey?

Fraction of Percentages

Age 14 to 16 Short Challenge Level:

What is $W$ as a fraction of $Z?$

Traffic Jam

Age 14 to 16 Short Challenge Level:

Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced?

Late for Work

Age 14 to 16 Short Challenge Level:

What average speed should Ms Fanthorpe drive at to arrive at work on time?

Backwards Laps

Age 14 to 16 Short 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?