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

### Multiplication Magic Square

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

### Tommy's Tankard

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

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

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

### Bouncing ball

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

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

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

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

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

### Magical Products

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

problem

### Three Blind Mice

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

### Second Half Score

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

problem

### Pride of Place

Two fractions have been placed on a number line. Where should another fraction be placed?

problem

### between a sixth and a twelfth

The space on a number line between a sixth and a twelfth is split into 3 equal parts. Find the number indicated.

problem

### Too Close to Call

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

A group of monkeys eat various fractions of a harvest of peanuts. What fraction is left behind?

problem

### Slightly Outnumbered

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

problem

### A Drink of Water

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

### Test Scores

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

### Tennis Club

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

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

To make porridge, Goldilocks mixes oats and wheat bran..... what percentage of the mix is wheat?

problem

### Entrance Exam

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

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

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

problem

### Bargain

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

Weekly Problem 10 - 2014

What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?

What is the sum of the first $2011$ digits when $20 \div 11$ is written as a decimal?

problem

### Solitare

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

### Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased by ?

problem

### Breakfast Time

Four hobbits each eat one quarter of the porridge remaining in the pan. How much is left?

problem

### Producing an Integer

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

problem

### Antiques Roadshow

Last year, on the television programme Antiques Roadshow... work out the approximate profit.

problem

### Elephants and geese

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

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?