Multi-Step Mixed Reasoning Challenge Set 4
A multi-step mixed reasoning challenge combines several maths skills, such as fractions, ratio, money and measures, into a single longer word problem that must be solved in stages, where the answer to one stage is needed to work out the next. 11+ papers use these longer 'reasoning challenge' questions to test whether pupils can plan a solution across several steps, not just apply one isolated skill, and they typically carry more marks than single-step questions.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole question through once without calculating, to understand the overall situation and what the final answer needs to be.
- Identify each separate calculation needed and the order they must be done in, since later steps often depend on earlier results.
- Write down each step's working clearly and label what each intermediate answer represents, such as 'cost so far' or 'amount remaining', so you do not lose track between steps.
- Carry exact values through the working from one step to the next, only rounding the very final answer if needed.
- After reaching a final answer, re-read the original question to check you have answered exactly what was asked, such as the change left rather than the total spent.
- If time allows, sanity-check your final answer by estimating roughly what size of answer the question should give.
Worked example
A charity bake sale raises 84 pounds. Two-thirds of the money raised is spent on ingredients for the next sale, and the remainder is split equally between 4 local charities. How much does each charity receive?
- Find the amount spent on ingredients: two-thirds of 84 = (84 / 3) x 2 = 28 x 2 = 56 pounds.
- Find the remaining amount: 84 - 56 = 28 pounds.
- Divide the remaining amount equally between 4 charities: 28 / 4 = 7.
- Each charity receives 7 pounds.
Practice questions
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Q1A school raises 150 pounds. Half is spent on new books and a quarter of what remains is spent on a trophy. How much is left after both purchases?Show answer
Answer: 56.25 pounds (75 spent on books, leaving 75, then 18.75 spent on the trophy, leaving 56.25)
Q2A recipe for 6 people needs 450 g of flour. How much flour is needed for 9 people, at the same rate?Show answer
Answer: 675 g (75 g per person x 9)
Q3A shop reduces a 60 pound jacket by 20 percent, then adds 5 percent VAT to the reduced price. What is the final price?Show answer
Answer: 50.40 pounds (60 x 0.8 = 48, then 48 x 1.05 = 50.40)
Q4A tank holds 200 litres and is 3/8 full. How many more litres are needed to fill it completely?Show answer
Answer: 125 litres (200 x 3/8 = 75 currently in the tank, 200 - 75 = 125 needed)
Q5Three friends share a bill in the ratio 2:3:5. If the total bill is 60 pounds, how much does the friend with the largest share pay?Show answer
Answer: 30 pounds (10 parts total, 6 pounds per part, 5 x 6 = 30)
Q6A car journey of 240 km is completed in two stages. The first stage takes 2 hours at 60 km/h. The second stage covers the remaining distance in 1.5 hours. Work out the average speed for the second stage.Show answer
Answer: 80 km/h (first stage covers 120 km, remaining 120 km in 1.5 hours, 120 / 1.5 = 80)
Q7A cinema sells tickets at 8 pounds for adults and 5 pounds for children. A group buys 3 adult and 4 child tickets, then uses a 10 pound voucher. How much do they pay in total?Show answer
Answer: 34 pounds (3 x 8 + 4 x 5 = 44, then 44 - 10 = 34)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A youth club has 120 pounds. It spends 3/5 of the money on new sports equipment. Of the remaining money, it spends 40 percent on refreshments for an event, and saves the rest. How much money does the club save?
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A factory produces 2,400 toys in a week. 5/8 of the toys are cars and the rest are trains. The cars are packed into boxes of 15, and the trains are packed into boxes of 12. Work out the total number of boxes needed for the whole week's production.
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Nothing ticked yet - 6 available
Free printable worksheet
Want more practice on paper? Download the multi-step mixed reasoning challenge set 4 worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 30 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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