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:


   
Stage 3 ★ Sheet 1 Solutions                 
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Stage 3 ★★ Sheet 1 Solutions      
  Sheet 2 Solutions      



Thunder and Lightning

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 20 - 2009
How far away was the lightning if the flash and the thunderclap were 6 seconds apart?

Printer Ink

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 2 - 2017
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

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 53 - 2009
Fred flew to Melbourne, Australia. What time was it in Melbourne when Fred's flight arrived?

Walking in the Mountains

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 5 - 2010
Heidi and Peter are walking through the mountains. They pass two signs which say how far away their destination is, so can you work out how long it will take them to get there?

A Leg to Stand On

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 30 - 2012
Can you work out the number of chairs at a cafe from the number of legs?

A Classy Ratio

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 12 - 2017
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

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 40 - 2007
Harriet Hare and Turbo Tortoise want to cross the finish line together on their 12 mile race.... What time should Harriet set off?

Speed over a Bridge

KS 3 Short Challenge Level:

Challenge Level:1

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

Tummy Ache

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 6 - 2012
Timmy, Tammy and Tommy all go to the doctors. In what order do they arrive at the surgery?

Dean's Mountain

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 20 - 2016
Dean runs up a mountain road at 8 km per hour. It takes him one hour to get to the top. He runs down the same mountain at 12 km per hour. How long does it take him to run down the mountain?

Stair Climb

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 16 - 2006
Three people run up stairs at different rates. If they each start from a different point - who will win, come second and come last?

Race Time

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 9 - 2010
Frank and Gabriel competed in a 200m race. Interpret the different units used for their times to work out who won.

Three of a Kind

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 16 - 2013
How long is it between 5:55 and the next time all three digits on a digital clock are the same?

Athletics Club

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 7 - 2017
An athletics club has girl, boy and adult members in the ratio 3:4:9. If there are 16 more adult members than junior members, how many members does the club have?

Minutes in Between

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 30 - 2008
How many minutes are there between 11:41 and 14:02?

Travelling by Train

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 27 - 2016
Stephen leaves Middlesborough by train at 09:00. The train travels the first 27km at 96km/h. It then stops at Darlington for 3 minutes, before travelling the remaining 29km to Durham at 96km/h. At what time does Stephen arrive at Durham?

Shepherd's Flock

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 26 - 2010
Does Joseph have too many sheep in his flock...

Dance Party

KS 3 Short Challenge Level:

Challenge Level:1

At a party, each man danced with exactly three women, and each woman danced with exactly two men. If 12 men attended the party, how many women attended?

Flapjack

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 37 - 2008
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?

Millenium Leap

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 18 - 2012
How many leap years will there be between 2001 and 3001?

24 Hour Conundrum

KS 3 Short Challenge Level:

Challenge Level:1

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

Tyre Wear

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 52 - 2008
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?

Caught in the Web

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 20 - 2012
Can you estimate the mass of insects caught by spiders in the UK each year?

Family Fortune

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 8 - 2007
If three brothers will get £20 more if they do not share their money with their sister, how much money is there?

Roman Distances

KS 3 Short Challenge Level:

Challenge Level:1

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?

Off the Cuff

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 23 - 2012
Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?

Hiking the Hill

KS 3 Short Challenge Level:

Challenge Level:1

Weekly Problem 22 - 2011
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?

Inches and Barleycorns

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

How many barleycorns are there in one inch?

Bike Shop

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 8 - 2013
If I walk to the bike shop, but then cycle back, what is my average speed?

Marathon Mission

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 33 - 2012
Minnie trained more for the London Marathon this year, so her speed increased. By what percentage did her time decrease?

Don't Be Late

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 31 - 2010
Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

Musical Maths

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Decimal Clock

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 51 - 2013
A decimal clock is started at midnight. What time would it show at 6 o'clock in the morning?

Sharing Sweets

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 41 - 2017
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?

Very Long Line

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 46 - 2016
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?

Fruit Basket Ratio

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Overtake

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 19 - 2011
Tom and Tim are travelling towards Glasgow, but leave at different times. If Tim overtakes Tom, how fast is he travelling?

Ratio Swap

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

How Many Swimmers

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 46 - 2017
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

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Revolutions

KS 3 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Weekly Problem 30 - 2006
Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?

The London Eye

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 18 - 2014
The 80 spokes of the giant wheel The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?

Tyneside Average Speed

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 12 - 2006
A van travels from Newcastle to South Shields at 30mph and returns at 40mph. What is its average speed?

Ratio Riddle

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 8 - 2006
Can you work out the ratio $b:c$ given the ratios $a:b$ and $a:c$.

Backwards Laps

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Crude Calculation

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

100m Sprint

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Travelator

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Hillwalking

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 40 - 2016
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?

Antifreeze

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 4 - 2007
How much more antifreeze is needed to make the proportion 30%?

Flower Show

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Traffic Jam

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 1 - 2017
Yesterday evening, Emily's journey home took 25% longer than usual. By what percentage was her average speed reduced compared to normal?

Platinum Puzzle

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 29 - 2007
What is the approximate total volume of platinum that has ever been produced?

Pond Runners

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Fraction of Percentages

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Televisual Technology

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

Television screens have changed from the traditional 4:3 to widescreen 16:9. If a new television and an old television have the same area, what is the ratio of their widths?

Day Out

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Petrol Stop

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Walk up the Escalator

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Boys and Girls

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Digging Holes

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

How long will it take one man and two dogs to dig 15 holes?

Laps

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Late for Work

KS 4 Short Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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