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# 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.

### Brothers and Sisters

### Turbo Tortoise

### Draining a Pool

### Dean's Mountain

### Race Time

### Athletics Club

### Speed over a Bridge

### Minutes in Between

### Family Fortune

### Flapjack

### Eating Beans

### 24 Hour Conundrum

### Roman Distances

### Thunder and Lightning

### Three of a Kind

### Printer Ink

### Flying Down Under

### A Classy Ratio

### Decimal Clock

### Off the Cuff

### Musical Maths

### The Elephant Diet

### Ratio Swap

### Don't Be Late

### Sharing Sweets

### Tyre Wear

### A Leg to Stand On

### Fruit Basket Ratio

### How Many Swimmers?

### Leg It

### Out of Sync

### Stair Climb

### Washing Elephants

### Revolutions

### Caught in the Web

### Honey Bees

### Tummy Ache

### Hiking the Hill

### The London Eye

### Antifreeze

### Inches and Barleycorns

### Travelling by Train

### Travelator

### Hillwalking

### Ratio Riddle

### Very Long Line

### Overtake

### Tyneside Average Speed

### Platinum Puzzle

### Pond Runners

### Dolly Dolphin

### Bike Shop

### Crude Calculation

### Walking in the Mountains

### Walk up the Escalator

### 100m Sprint

### Flower Show

### Boys and Girls

### Televisual Technology

### Laps

### Two Trains

### Traffic Jam

### Late for Work

### Backwards Laps

### Day Out

### Petrol Stop

### Marathon Mission

Or search by topic

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.

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

Harriet Hare and Turbo Tortoise want to cross the finish line together on their 12 mile race.... What time should Harriet set off?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

Albert Einstein could see two clocks which were out of sync. For what fraction of the day did they show the same time?

Age 11 to 14

ShortChallenge 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?

Age 11 to 14

ShortChallenge Level

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

Age 11 to 14

ShortChallenge Level

Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

How many barleycorns are there in one inch?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

Can you work out the average speed of the van?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge 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?

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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

Age 14 to 16

ShortChallenge Level

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