Multi-Step Reasoning Challenge Set 2
Multi-Step Reasoning Challenge Set 2 extends multi-step problem-solving to questions with three or more linked steps, often combining fractions, percentages and the four operations within a single scenario. It follows on from the first Multi-Step Reasoning Challenge topic and is aimed at pupils who can already plan and complete a two-step calculation confidently.
Method
- Read the whole problem twice before calculating anything, and count how many separate facts or quantities are given, since a longer problem usually needs a step for each one.
- Decide the order the steps must happen in, since some information can only be used once an earlier step has been completed.
- Write down each intermediate result with a short label, such as 'money left after step 1', so a later step cannot be applied to the wrong number.
- Where a problem mixes fractions, percentages and whole-number operations, convert each one to the same form, such as a decimal, before combining them if that makes the arithmetic easier.
- Complete the calculation one labelled step at a time, checking that each intermediate answer is a sensible size before moving on.
- On the final step, reread the question to check exactly what quantity is being asked for, since the last number you calculate is not always the final answer required.
Worked example
A library has 240 books. On Monday, 1/4 of the books are borrowed. On Tuesday, 20% of the remaining books are borrowed. On Wednesday, 18 more books are returned. How many books are in the library at the end of Wednesday?
- Find the number of books borrowed on Monday: 1/4 of 240 = 60.
- Find the number remaining after Monday: 240 - 60 = 180.
- Find the number borrowed on Tuesday: 20% of 180 = 36.
- Find the number remaining after Tuesday: 180 - 36 = 144.
- Add the 18 books returned on Wednesday: 144 + 18.
- The final answer is 162 books.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A shop has 160 T-shirts. It sells 2/5 of them in a morning sale, then 25% of what remains in an afternoon sale. How many T-shirts are left?Show answer
Answer: 72 T-shirts (2/5 of 160 = 64 sold, leaving 96; 25% of 96 = 24 sold, leaving 72)
Q2Tom has 80 pounds. He spends 30% of it on a jacket, then 1/4 of what remains on a book. How much does he have left?Show answer
Answer: 42 pounds (80 - 24 = 56 after the jacket; 56 - 14 = 42 after the book)
Q3A tank contains 500 litres of water. Half of the water is drained, then 40% of what remains is drained again, then 45 litres are added back. How much water is in the tank now?Show answer
Answer: 195 litres (500 - 250 = 250; 250 - 100 = 150; 150 + 45 = 195)
Q4A charity raises 720 pounds. It gives 1/3 to one cause, then splits the remainder equally between 6 other causes, before adding a further 60 pounds from a separate donation to just one of those 6 causes. How much does that one cause receive in total?Show answer
Answer: 140 pounds (720 - 240 = 480 remaining; 480 / 6 = 80 each; 80 + 60 = 140)
Q5A school has 320 pupils. 45% of them are boys. Of the boys, 1/4 walk to school. How many boys walk to school?Show answer
Answer: 36 boys (45% of 320 = 144 boys; 1/4 of 144 = 36)
Q6A baker makes 240 loaves. She sells 5/8 of them in the morning. Of the loaves left, 30% are sold in the afternoon, and the rest are given to a food bank. How many loaves go to the food bank?Show answer
Answer: 63 loaves (240 - 150 = 90 remaining after the morning; 30% of 90 = 27; 90 - 27 = 63)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A carton contains 480 ml of juice. Priya drinks 1/4 of it, then her brother drinks 30% of what remains. How much juice is left in the carton?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A shop orders 360 phone cases. It sells 40% of them in the first week. Of the cases remaining, 2/3 are sold in the second week. The rest are put on clearance at half price. (a) Calculate how many cases are put on clearance. (b) If each clearance case originally cost 12 pounds, calculate the total clearance revenue if every clearance case sells at half price.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
A youth club has 200 members. 55% of the members are girls, and the rest are boys. Of the girls, 2/5 attend the Friday session; of the boys, 1/3 attend the Friday session. (a) Calculate the number of girls and the number of boys in the club. (b) Calculate how many girls and how many boys attend the Friday session. (c) Calculate the total number of members attending the Friday session.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 5 available
Free printable worksheet
Want more practice on paper? Download the multi-step reasoning challenge set 2 worksheet pack - 11 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 8 of 11+ Maths Workbook 4, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on multi-step reasoning challenge set 2, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.