Worded Problems Set D
Worded Problems Set D develops the general skill of turning a written scenario into the right sequence of calculations, without the question naming the operations directly. 11+ papers deliberately disguise the arithmetic inside everyday contexts, such as shopping, travel and events, so pupils must decide what to calculate, in what order, before any working can begin.
Method
- Read the whole problem twice before calculating anything, so you know exactly what final answer is being asked for.
- Underline or note the key numbers and the words that signal an operation, for example 'altogether' for adding, 'shared equally' for dividing, or 'more than' for a difference.
- For multi-step problems, break the question into separate, clearly ordered steps rather than trying to combine everything into one calculation.
- Choose an efficient written or mental method for each individual step.
- Where a real-world context requires rounding, decide sensibly whether to round up or down, for example rounding up when working out how many vehicles are needed for a group.
- Reread the question at the end to check you have answered exactly what was asked, rather than stopping at an intermediate value.
Worked example
A youth club has 96 members. On a residential trip, 3/8 of the members go by coach and the rest go by minibus, with each minibus holding 9 people. How many minibuses are needed?
- Find the number travelling by coach: 3/8 x 96 = 36.
- Find the number travelling by minibus: 96 - 36 = 60.
- Divide by the minibus capacity: 60 / 9 = 6 remainder 6.
- Since 6 people still need transport, an extra minibus is needed even though it will not be full.
- Final answer: 7 minibuses.
Practice questions
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Q1A baker has 250 g of butter. A recipe needs 40 g of butter per batch of biscuits. How many complete batches can she make?Show answer
Answer: 6 complete batches (250 / 40 = 6 remainder 10)
Q2Liam has 3.50 pounds. Sweets cost 0.35 pounds each. How many sweets can he buy?Show answer
Answer: 10 (3.50 / 0.35)
Q3A coach set off with 52 passengers. At the first stop, 18 got off and 11 got on. How many passengers are now on the coach?Show answer
Answer: 45 (52 - 18 + 11)
Q4A charity needs to raise 500 pounds and has so far raised 3/5 of this target. How much more does it need to raise?Show answer
Answer: 200 pounds (3/5 x 500 = 300 raised, 500 - 300 = 200 still needed)
Q5Tickets for a concert cost 14 pounds each. A group buys 6 tickets and pays with two 50 pound notes. What change do they get?Show answer
Answer: 16 pounds (6 x 14 = 84, 100 - 84 = 16)
Q6A tank contains 45 litres of water. A pump removes 3 litres every minute. After how many minutes will the tank be empty?Show answer
Answer: 15 minutes (45 / 3)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A printing company charges 25 pounds for the first 100 flyers, then 8 pounds for every additional 50 flyers. Kofi orders 350 flyers. How much does he pay in total? Show your working.
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A farmer has 160 sheep. He sells 1/4 of them at market, then buys 40 more lambs. Two weeks later, 15% of his new total are moved to a different field. How many sheep remain in the original field? Show each step of your working.
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Free printable worksheet
Want more practice on paper? Download the worded problems set d worksheet pack - 9 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 13 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
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