Fractions, Decimals, Percentages and Ratio - Short Problems

This is part of our collection of Short Problems.

You may also be interested in our longer problems on Fractions, Decimals Percentages and Ratio.

Printable worksheets containing selections of these problems are available here:

 Stage 3 ★ Sheet 1 Solutions Stage 4 ★★ Sheet 1 Solutions Sheet 2 Solutions Sheet 3 Solutions

Petrol Station

KS 2 & 3 Short Challenge Level:

Weekly Problem 15 - 2011
Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?

Magical Products

KS 2 & 3 Short Challenge Level:

Weekly Problem 9 - 2013
Can you place the nine cards onto a 3x3 grid such that every row, column and diagonal has a product of 1?

Valuable Percentages

KS 2 & 3 Short Challenge Level:

Weekly Problem 23 - 2010
These numbers have been written as percentages. Can you work out which has the greatest value?

Shepherd's Flock

KS 2 & 3 Short Challenge Level:

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

Restful Sundays

KS 2 & 3 Short Challenge Level:

Weekly Problem 17 - 2006
Granny says she is 84 years old, not counting her Sundays. How old is she?

Printer Ink

KS 3 Short Challenge Level:

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.

Inspector Remorse

KS 3 Short Challenge Level:

Weekly Problem 49 - 2011
How long will it take Inspector Remorse to crack this crime spree?

Pride of Place

KS 3 Short Challenge Level:

Weekly Problem 47 - 2010
Two fractions have been placed on a number line. Where should another fraction be placed?

Chocolate Multipliers

KS 3 Short Challenge Level:

Weekly Problem 23 - 2006
Can you work out how many times more chocolate Peg has then Meg?

Washing-up

KS 3 Short Challenge Level:

Weekly Problem 34 - 2016
A survey for washing-up liquid revealed that 2/3 of customers bought Jinx, and 1/3 of customers bought Kleenz. After an advertising campaign, what fraction of customers buy Kleenz?

Mean Sequence

KS 3 Short Challenge Level:

Weekly Problem 38 - 2009
This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?

Squeezed In

KS 3 Short Challenge Level:

Weekly Problem 9 - 2017
What integer x makes x/9 lie between 71/7 and 113/11?

Tommy's Tankard

KS 3 Short Challenge Level:

Weekly Problem 4 - 2017
Tommy's tankard holds 480ml when it is one quarter empty. How much does it hold when it is one quarter full?

Off the Cuff

KS 3 Short Challenge Level:

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?

The Grand Old Duke of York

KS 3 Short Challenge Level:

Weekly Problem 44 - 2017
What percentage of his 10,000 men did the Grand Old Duke of York have left when he arrived back at the bottom of the hill?

KS 3 Short Challenge Level:

Weekly Problem 43 - 2013
What is 20% of 30% of 40% of £50?

Information Display

KS 3 Short Challenge Level:

Weekly Problem 7 - 2008
The information display on a train shows letters by illuminating dots in a rectangular array. What fraction of the dots in this array is illuminated?

Talulah's Tulips

KS 3 Short Challenge Level:

Weekly Problem 10 - 2017
Talulah plants some tulip bulbs. When they flower, she notices something interesting about the colours. What fraction of the tulips are white?

Squares in a Square

KS 3 Short Challenge Level:

Weekly Problem 43 - 2016
In the diagram, the small squares are all the same size. What fraction of the large square is shaded?

Better Spelling

KS 3 Short Challenge Level:

Weekly Problem 12 - 2010
Can Emily increase her average test score to more than $80$%? Find out how many more tests she must take to do so.

How Many Swimmers

KS 3 Short Challenge Level:

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?

Tennis Club

KS 3 Short Challenge Level:

Weekly Problem 6 - 2007
Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?

Multiplication Magic Square

KS 3 Short Challenge Level:

Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?

Meeting Point

KS 3 Short Challenge Level:

Weekly Problem 32 - 2008
Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?

A Classy Ratio

KS 3 Short Challenge Level:

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?

Almost Half Way

KS 3 Short Challenge Level:

Weekly Problem 26 - 2012
Which of these fractions is the largest?

Family Fortune

KS 3 Short Challenge Level:

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?

Second Half Score

KS 3 Short Challenge Level:

Weekly Problem 48 - 2016
Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?

Percentage of a Quarter

KS 3 Short Challenge Level:

Weekly Problem 50 - 2017
What percentage of a quarter is a fifth?

Flapjack

KS 3 Short Challenge Level:

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?

Smashing Time

KS 3 Short Challenge Level:

Weekly Problem 58 - 2012
Once granny has smashed some of her cups and saucers, how many cups are now without saucers?

Three Blind Mice

KS 3 Short Challenge Level:

Weekly Problem 10 - 2013
Each of the three blind mice in turn ate a third of what remained of a piece of cheese. What fraction of the cheese did they eat in total?

Porridge

KS 3 Short Challenge Level:

Weekly Problem 43 - 2006
To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?

Breakfast Time

KS 3 Short Challenge Level:

Weekly Problem 49 - 2016
Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?

Half Way

KS 3 Short Challenge Level:

Weekly Problem 24 - 2010
Can you find a number that is half way between these two fractions?

Test Scores

KS 3 Short Challenge Level:

Weekly Problem 10 - 2016
Ivan, Tibor and Alex sat a test and achieved 85%, 90% and 95% respectively. Tibor scored just one more mark than Ivan. How many marks did Alex get?

Question Setters

KS 3 Short Challenge Level:

Weekly Problem 44 - 2008
John, Peter, Rudolf, Susie and Tony decide to set some questions for the Schools Mathematical Challenge. Can you work out how long in total they spend setting questions?

Itchy's Fleas

KS 3 Short Challenge Level:

Weekly Problem 32 - 2017
Itchy has a million fleas. His anti-flea leaves no more than 1% of the original fleas after use. What is the least number of fleas that the shampoo will remove?

A Leg to Stand On

KS 3 Short Challenge Level:

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

Bargain

KS 3 Short Challenge Level:

Weekly Problem 11 - 2013
A shop has "Everything half price", and then "15% off sale prices". What is the overall reduction in cost?

Peter Piper

KS 3 Short Challenge Level:

Weekly Problem 21 - 2016
Peter Piper picked a peck of pickled peppers. How many more pecks must Peter Piper pick to fill a barrel?

Tyre Wear

KS 3 Short Challenge Level:

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?

Athletics Club

KS 3 Short Challenge Level:

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?

Baby Boom

KS 3 Short Challenge Level:

Weekly Problem 25 - 2012
Which of the cities shown had the largest percentage increase in population?

Marathon Mission

KS 3 Short Challenge Level:

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

Spider Solitare

KS 3 Short Challenge Level:

Weekly Problem 45 - 2014
After playing 500 games, my success rate at Spider Solitare is 49%. How many games do I need to win to increase my success rate to 50%?

Pied Piper

KS 3 Short Challenge Level:

Weekly Problem 7 - 2007
How many rats did the Pied Piper catch?

Slightly Outnumbered

KS 3 Short Challenge Level:

Weekly Problem 3 - 2010
If this class contains between $45$% and $50$% girls, what is the smallest possible number of girls in the class?

Traffic Jam

KS 3 Short Challenge Level:

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?

Too Close to Call

KS 3 Short Challenge Level:

Weekly Problem 24 - 2012
Can you put these very close fractions into order?

Fractions of 1000

KS 3 & 4 Short Challenge Level:

Weekly Problem 50 - 2010
Find a simple way to compute this long fraction.

Square Percentage

KS 3 & 4 Short Challenge Level:

Weekly Problem 36 - 2016
What percentage of the integers between 1 and 10,000 are square numbers?

Ordering Fractions

KS 3 & 4 Short Challenge Level:

Weekly Problem 46 - 2014
Which of these powers of fractions has greatest value?

Star in a Hexagon

KS 3 & 4 Short Challenge Level:

Weekly Problem 20 - 2017
The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?

Producing an Integer

KS 3 & 4 Short Challenge Level:

Weekly Problem 46 - 2011
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

2011 Digits

KS 3 & 4 Short Challenge Level:

Weekly Problem 10 - 2014
What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?

KS 4 Short Challenge Level:

Weekly Problem 51 - 2007
Last year, on the television programme Antiques Roadshow... work out the approximate profit.

A Drink of Water

KS 4 Short Challenge Level:

Weekly Problem 43 - 2015
Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?

Ratio Riddle

KS 4 Short Challenge Level:

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

Percentage Swap

KS 4 Short Challenge Level:

Weekly Problem 47 - 2007
What is 50% of 2007 plus 2007% of 50?

Recurring Mean

KS 4 Short Challenge Level:

Weekly Problem 49 - 2007
What is the mean of 1.2 recurring and 2.1 recurring?

Antifreeze

KS 4 Short Challenge Level:

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

Flower Show

KS 4 Short Challenge Level:

Weekly Problem 7 - 2006
It takes four gardeners four hours to dig four circular flower beds, each of diameter 4 metres. How long will it take six gardeners to dig six circular flower beds, each of diameter six metres?