This is part of our collection of Short Problems.
You may also be interested in our longer problems on Fractions, Decimals and Percentages.
Printable worksheets containing selections of these problems are available here.
problem
Tommy's Tankard
Age
11 to 14
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?
Tommy's tankard holds 480ml when it is one quarter empty. How much does it hold when it is one quarter full?
problem
Smashing Time
Age
11 to 14
Challenge level
Weekly Problem 58 - 2012
Once granny has smashed some of her cups and saucers, how many cups are now without saucers?
Once granny has smashed some of her cups and saucers, how many cups are now without saucers?
problem
Talulah's Tulips
Age
11 to 14
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?
Talulah plants some tulip bulbs. When they flower, she notices something interesting about the colours. What fraction of the tulips are white?
problem
Percentage Mad
Age
11 to 14
Challenge level
Weekly Problem 43 - 2013
What is 20% of 30% of 40% of £50?
problem
Bouncing Ball
Age
11 to 14
Challenge level
A ball is dropped from a height, and every time it hits the ground, it bounces to 3/5 of the height from which it fell.
problem
Information Display
Age
11 to 14
Challenge level
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?
problem
Mean Sequence
Age
11 to 14
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?
This sequence is given by the mean of the previous two terms. What is the fifth term in the sequence?
problem
Better Spelling
Age
11 to 14
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.
Can Emily increase her average test score to more than $80$%? Find out how many more tests she must take to do so.
problem
Valuable Percentages
Age
11 to 14
Challenge level
Weekly Problem 23 - 2010
These numbers have been written as percentages. Can you work out which has the greatest value?
These numbers have been written as percentages. Can you work out which has the greatest value?
problem
Ordering Fractions
Age
11 to 14
Challenge level
Weekly Problem 46 - 2014
Which of these fractions has greatest value?
Which of these fractions has greatest value?
problem
Multiplication Magic Square
Age
11 to 14
Challenge level
Weekly Problem 32 - 2015
Can you work out the missing numbers in this multiplication magic square?
Can you work out the missing numbers in this multiplication magic square?
problem
Second Half Score
Age
11 to 14
Challenge level
Boarwarts Academy played their annual match against Range Hill School. What fraction of the points were scored in the second half?
problem
Halfway
Age
11 to 14
Challenge level
Can you find a number that is halfway between two fractions?
problem
Pride of Place
Age
11 to 14
Challenge level
Two fractions have been placed on a number line. Where should another fraction be placed?
problem
Between a Sixth and a Twelfth
Age
11 to 14
Challenge level
The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.
problem
Magical Products
Age
11 to 14
Challenge level
Can you place the nine cards onto a 3×3 grid such that every row, column and diagonal has a product of 1?
problem
Three Blind Mice
Age
11 to 14
Challenge level
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?
problem
Too Close to Call
Age
11 to 14
Challenge level
Weekly Problem 24 - 2012
Can you put these very close fractions into order?
Can you put these very close fractions into order?
problem
Peanut Harvest
Age
11 to 14
Challenge level
A group of monkeys eat various fractions of a harvest of peanuts. What fraction is left behind?
problem
Tricky Fractions
Age
11 to 14
Challenge level
Use this series of fractions to find the value of x.
problem
Slightly Outnumbered
Age
11 to 14
Challenge level
If this class contains between $45$% and $50$% girls, what is the smallest possible number of girls in the class?
problem
Test Scores
Age
14 to 16
Challenge level
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?
problem
Baby Boom
Age
14 to 16
Challenge level
Which of the cities shown had the largest percentage increase in population?
problem
Tennis Club
Age
14 to 16
Challenge level
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?
problem
The Grand Old Duke of York
Age
14 to 16
Challenge level
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?
problem
Porridge
Age
14 to 16
Challenge level
To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?
problem
Entrance Exam
Age
14 to 16
Challenge level
Dean finishes his exam strongly. Can you work out how many questions are on the paper if he gets an average of 80%?
problem
Meeting Point
Age
14 to 16
Challenge level
Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?
problem
Petrol Station
Age
14 to 16
Challenge level
Andrea has just filled up a fraction of her car's petrol tank. How much petrol does she now have?
problem
A Drink of Water
Age
14 to 16
Challenge level
Weekly Problem 43 - 2015
Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?
Rachel and Ross share a bottle of water. Can you work out how much water Rachel drinks?
problem
Percentage Unchanged
Age
14 to 16
Challenge level
If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?
problem
Washing-Up
Age
14 to 16
Challenge level
What fraction of customers buy Kleenz after the advertising campaign?
problem
Breakfast Time
Age
14 to 16
Challenge level
Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?
problem
Itchy's Fleas
Age
14 to 16
Challenge level
Itchy the dog has a million fleas. How many fleas might his shampoo kill?
problem
Percentage of a Quarter
Age
14 to 16
Challenge level
What percentage of a quarter is a fifth?
problem
Recurring Mean
Age
14 to 16
Challenge level
What is the mean of 1.2 recurring and 2.1 recurring?
problem
Fractions of 1000
Age
14 to 16
Challenge level
Find a simple way to compute this long fraction.
problem
Bargain
Age
14 to 16
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?
A shop has "Everything half price", and then "15% off sale prices". What is the overall reduction in cost?
problem
2011 Digits
Age
14 to 16
Challenge level
Weekly Problem 10 - 2014
What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?
problem
Solitare
Age
14 to 16
Challenge level
After playing 500 games, my success rate at Solitare is 49%. How many games do I need to win to increase my success rate to 50%?
problem
Producing an Integer
Age
14 to 16
Challenge level
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?
problem
Squeezed In
Age
14 to 16
Challenge level
Weekly Problem 9 - 2017
What integer x makes x/9 lie between 71/7 and 113/11?
What integer x makes x/9 lie between 71/7 and 113/11?
problem
Antiques Roadshow
Age
14 to 16
Challenge level
Last year, on the television programme Antiques Roadshow... work out the approximate profit.
problem
Elephants and Geese
Age
14 to 16
Challenge level
Yesterday, at Ulaanbaatar market, a white elephant cost the same amount as 99 wild geese. How many wild geese cost the same amount as a white elephant today?
problem
The Property Market
Age
14 to 16
Challenge level
A property developer sells two houses, and makes a 20% loss on one and a 20% profit on the other. Overall, did he make a profit or a loss?