Practise 28 exam-style questions on Fractions in ratio problems for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
28 questions
1–5 marks each
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20 questions, marked as you go
Sample questions with model answers
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
Question 1
2 marks
A box contains red, blue and green beads in the ratio 2 : 3 : 7.
What fraction of the beads are not blue? Give your answer in its simplest form.
Model answer
Total parts \(= 2 + 3 + 7 = 12\) Not blue \(= 2 + 7 = 9\) parts Fraction \(= \dfrac{9}{12} = \dfrac{3}{4}\)
Explanation
Add the parts to find the whole: 12 parts. The beads that are not blue are the red and green ones, 9 parts. Then simplify \(\dfrac{9}{12}\) by dividing top and bottom by 3.
Mark scheme
1 mark
M1 for a total of 12 parts used, e.g. \(\dfrac{3}{12}\) or \(\dfrac{9}{12}\)
correct answer with no working scores full marks
1 mark
A1 for \(\dfrac{3}{4}\)
accept \(\dfrac{9}{12}\) for M1 A0
Question 2
2 marks
Tom's height is \(\dfrac{4}{5}\) of his dad's height. Tom's dad is 30 cm taller than Tom.
How tall is Tom?
Model answer
Tom : dad = 4 : 5 The difference is 1 part = 30 cm. Tom \(= 4 \times 30 = 120\) cm
Explanation
Tom is \(\dfrac{4}{5}\) of his dad's height, so the difference is the remaining \(\dfrac{1}{5}\), which is 30 cm. Tom is 4 of these fifths. Check: his dad is 150 cm and \(\dfrac{4}{5}\) of 150 is 120.
Mark scheme
1 mark
M1 for recognising the difference of 30 cm is \(\dfrac{1}{5}\) of his dad's height (or 1 part of 4 : 5), e.g. dad \(= 5 \times 30 = 150\)
correct answer with no working scores full marks
1 mark
A1 for 120 (cm)
cao
Question 3
3 marks
In a box of chocolates, \(\dfrac{3}{7}\) of the chocolates are milk chocolates. The rest are dark chocolates and white chocolates in the ratio 3 : 1. There are 6 white chocolates.
How many chocolates are in the box?
Model answer
Dark : white = 3 : 1, so dark and white together \(= 4 \times 6 = 24\) chocolates. These are \(1 - \dfrac{3}{7} = \dfrac{4}{7}\) of the box. \(\dfrac{1}{7}\) of the box \(= 24 \div 4 = 6\) Total \(= 7 \times 6 = 42\)
Explanation
White chocolates are 1 of the 4 parts of the non-milk chocolates, which are \(\dfrac{4}{7}\) of the box, so white chocolates are \(\dfrac{1}{7}\) of the box. Check: 18 milk, 18 dark and 6 white make 42, and 18 is \(\dfrac{3}{7}\) of 42.
Mark scheme
1 mark
P1 for \(\dfrac{4}{7}\) of the chocolates are not milk, or dark and white together \(= 4 \times 6 = 24\)
correct answer with no working scores full marks
1 mark
P1 for white \(= \dfrac{1}{4} \times \dfrac{4}{7} = \dfrac{1}{7}\), or 24 is \(\dfrac{4}{7}\) of the box
1 mark
A1 for 42
cao
Question 4
4 marks
The ratio of Amy's money to Ben's money is 5 : 3. Amy spends \(\dfrac{3}{5}\) of her money. Ben spends £12. They now have the same amount of money.
How much money did Amy have at the start?
Model answer
Amy \(= 5x\), Ben \(= 3x\) Amy spends \(\dfrac{3}{5} \times 5x = 3x\), so she has \(2x\) left. Ben has \(3x - 12\) left. \(3x - 12 = 2x\), so \(x = 12\) Amy had \(5 \times 12 = £60\)
Explanation
Represent the shares with one letter. Amy keeps \(\dfrac{2}{5}\) of her 5 parts, which is 2 parts; Ben's 3 parts minus £12 must equal this. Check: Amy £60 spends £36 leaving £24; Ben £36 spends £12 leaving £24.
Mark scheme
1 mark
P1 for Amy \(= 5x\) and Ben \(= 3x\)
oe; correct answer with no working scores full marks
1 mark
P1 for Amy has \(2x\) left
1 mark
P1 for \(3x - 12 = 2x\)
or 1 part = £12
1 mark
A1 for £60
cao
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