Twelve 11+ maths word problems, with a full worked solution under every one. Everything here is free and there's nothing to sign up for.
Jump to the printable PDFsThe questions are split across three difficulty levels — the same ones we use in our app, 11+ Heroes. The Challenge questions are pitched at 11+ exam difficulty (and sometimes a little beyond).
Worth saying before you start: if your child can do the arithmetic but freezes on questions like these, the problem usually isn't the maths. It's the step before it, where a sentence has to be turned into a plan. I've written separately about why children get stuck on word problems, which is worth reading alongside this if the same kind of mistake keeps recurring.
Each solution explains the reasoning rather than just stating the answer. A wrong attempt should tell you something about what your child was thinking.
There's a printable version at the bottom of the page.
Foundation
Foundation · Question 1
A box holds \( 24 \) chocolates. Ben eats \( \dfrac{1}{3} \) of them, and then gives \( 4 \) chocolates to his sister. How many chocolates are left in the box?
Answer: \( 12 \)
Step 1 — Ben eats \( \dfrac{1}{3} \) of \( 24 \), which is \( 8 \) chocolates, leaving \( 24 - 8 = 16 \).
Step 2 — He gives \( 4 \) to his sister: \( 16 - 4 = 12 \). So, there are \( 12 \) chocolates left.
Foundation · Question 2
A knight is gathering supplies. He buys \( 3 \) torches at \( £4 \) each and a coil of rope for \( £7 \). He pays the shopkeeper with a \( £20 \) note. How much change should the knight receive?
Answer: \( £1 \)
Step 1 — Cost of the torches: \( 3 \times £4 = £12 \).
Step 2 — Add the rope: \( £12 + £7 = £19 \).
Step 3 — Change from the note: \( £20 - £19 = £1 \). So, the knight gets \( £1 \) change.
Foundation · Question 3
Maya's tennis lesson starts at \( 4{:}20 \) in the afternoon and lasts \( 45 \) minutes. After the lesson, she spends another \( 15 \) minutes practising with a friend. At what time is Maya ready to leave?
Answer: \( 5{:}20 \)
Start at \( 4{:}20 \). After the \( 45 \)-minute lesson: \( 4{:}20 \) + \( 45 \) min = \( 5{:}05 \). After \( 15 \) minutes practising with the friend: \( 5{:}05 \) + \( 15 \) min = \( 5{:}20 \). So, Maya is ready to leave at \( 5{:}20 \).
Foundation · Question 4
A dragon's vault contains \( 40 \) golden goblets. The dragon gives away half of the goblets to a passing wizard, and then carefully polishes \( 3 \) of the goblets that are left. How many of the dragon's goblets have NOT yet been polished?
Answer: \( 17 \)
First, the dragon gives away half, so half remain: \( 40 \div 2 = 20 \) goblets left in the vault.
Then, of those, \( 3 \) are polished, so the number not yet polished is \( 20 - 3 = 17 \). The answer is \( 17 \) goblets.
Core
Core · Question 5
Two pirates share \( 56 \) gold coins in the ratio \( 3 : 5 \). How many more coins does the pirate with the larger share receive than the other pirate?
Answer: \( 14 \)
The ratio \( 3 : 5 \) has \( 3 + 5 = 8 \) parts, so each part is \( 56 \div 8 = 7 \) coins. The shares are \( 3 \times 7 = 21 \) and \( 5 \times 7 = 35 \) coins. So, the difference is \( 35 - 21 = 14 \) coins.
Core · Question 6
A recipe needs \( 250\text{g} \) of sugar. Sam has a \( 2\text{kg} \) bag of sugar and makes the recipe \( 3 \) times. How much sugar is left in the bag? Give your answer in grams.
Answer: \( 1250\text{g} \)
First convert: \( 2\text{kg} = 2000\text{g} \).
The recipe is made \( 3 \) times, using \( 3 \times 250\text{g} = 750\text{g} \).
So, the sugar left is: \( 2000\text{g} - 750\text{g} = 1250\text{g} \)
Core · Question 7
A farmer harvests \( 240 \) pumpkins from his field. He sells \( \dfrac{1}{3} \) of the whole harvest at the market, and gives \( \dfrac{1}{4} \) of the whole harvest to his neighbours. He keeps every pumpkin that is left to make soup. How many pumpkins does the farmer keep for soup?
Answer: \( 100 \)
Reading the question carefully, we can see that both fractions are taken from the original \( 240 \) pumpkins.
Sold: \( \dfrac{1}{3} \) of \( 240 = 80 \).
Given away: \( \dfrac{1}{4} \) of \( 240 = 60 \).
Kept for soup: \( 240 - 80 - 60 = 100 \). The answer is \( 100 \) pumpkins.
Core · Question 8
Leo wants to buy a bicycle that costs \( £100 \). He has already saved \( £30 \), and he saves a further \( £6 \) each week from his pocket money. How many more full weeks must Leo save before he can afford the bicycle?
Answer: \( 12 \)
Step 1 — Work out how much more Leo needs: \( £100 - £30 = £70 \).
Step 2 — Divide by his weekly saving: \( £70 \div £6 = 11 \) remainder \( 4 \). This means that after 11 weeks, Leo has saved \( £66 \), but is still \( £4 \) short. So, Leo must save for an additional week, giving \( 12 \) more weeks overall.
Challenge
Challenge · Question 9
A games console is priced at \( £240 \). It is reduced by \( 25\% \) in a sale. A shopper also has a voucher that takes off a further \( 10\% \) from the sale price. How much does the shopper pay for the console in total?
Answer: \( £162 \)
Apply the reductions one after the other.
Sale price: \( 25\% \) of \( £240 \) is \( £60 \), so \( £240 - £60 = £180 \).
The voucher then takes \( 10\% \) off this sale price: \( 10\% \) of \( £180 \) is \( £18 \), so \( £180 - £18 = £162 \). The shopper pays \( £162 \).
A key note from carefully reading the question is that the \( 10\% \) comes off the reduced price, not the original.
Challenge · Question 10
A merchant begins the day with a chest of silver coins. During the morning he doubles the number of coins he has by selling rare spices. In the afternoon, he spends \( 70 \) coins on fresh supplies. By the evening he has exactly \( 150 \) coins left. How many coins did the merchant have at the very start of the day?
Answer: \( 110 \)
We can work backwards, undoing each step in reverse order.
First, we undo the spending by adding it back: \( 150 + 70 = 220 \) coins.
Then, we undo the doubling by halving: \( 220 \div 2 = 110 \). So, he had \( 110 \) coins at the start of the day!
To check our answer, we can go forwards: \( 110 \) doubled is \( 220 \), minus \( 70 \) leaves \( 150 \). The merchant started with \( 110 \) coins.
Challenge · Question 11
A band of \( 100 \) adventurers must cross a wide river to continue their expedition. Each boat can carry up to \( 8 \) people, but \( 1 \) of those seats must always be taken by a boatman (who is not one of the adventurers) to row the boat across. Assuming that a boat can't be reused, what is the smallest number of boats the band needs so that every adventurer gets across?
Answer: \( 15 \)
Each boat holds \( 8 \), but \( 1 \) seat is the boatman, so only \( 7 \) adventurers can cross per boat. Divide: \( 100 \div 7 = 14 \) remainder \( 2 \). So \( 14 \) boats carry \( 98 \) adventurers, leaving \( 2 \) still waiting — one more boat is needed for those \( 2 \)!
Hence, the smallest number of boats needed is \( 15 \).
Challenge · Question 12
The great dragon Pyraxis returns to her vault after a fierce battle to count what remains of her treasure. During the year she spent \( \dfrac{2}{5} \) of her gold coins repairing the scorched walls of her cave, and later she rewarded her most loyal goblins with \( 90 \) gold coins. Counting what is left, she finds exactly \( 150 \) gold coins remaining. How many gold coins were in Pyraxis's vault at the very beginning?
Answer: \( 400 \)
Work backwards, undoing the steps in reverse order. The \( 90 \) coins to the goblins were given away last, so we add them back first: \( 150 + 90 = 240 \).
These \( 240 \) coins are what was left after Pyraxis spent \( \dfrac{2}{5} \) of her gold, so they must be the other \( \dfrac{3}{5} \) of the original vault.
Find one fifth: \( 240 \div 3 = 80 \).
The whole vault is five fifths: \( 80 \times 5 = 400 \).
We can also check our answer by going forwards again: \( \frac{2}{5} \) of \( 400 \) is \( 160 \) spent, leaving \( 240 \); minus \( 90 \) for the goblins leaves \( 150 \). \( \checkmark \)
Printable version
The questions and the worked solutions are separate PDFs, so you can hand over one without giving away the other. The questions sheet leaves space for working too!
Questions (PDF)Worked solutions (PDF)Want more like these?
These twelve come from our Word Problems exercise, which works through questions like these in graded difficulty and shows the full worked solution after every one.
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