Ratios
Ratio, proportion and rates of change
- Foundation
- Non-calculator
- 8 questions
- 29 marks
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
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Simplify $18:24$.
2 marks
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Share £$40$ in the ratio $1:4$.
2 marks
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Share £$90$ in the ratio $2:3:4$.
3 marks
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The ratio of boys to girls is $3:5$. There are $24$ boys. How many girls are there, and how many students are there altogether?
3 marks
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A map has scale $1:25000$. A distance on the map is $8$ cm. Find the real distance in kilometres.
4 marks
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Purple paint is made from blue and red in the ratio $5:2$. How much red is needed with $15$ litres of blue? How much blue is needed to make $21$ litres of purple paint?
4 marks
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Amy and Ben share some money in the ratio $4:5$. Ben receives £$12$ more than Amy. How much does each person receive?
5 marks
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A drink is made from juice and water in the ratio $2:5$. How much water is mixed with $180$ ml of juice? More juice is added so that the ratio becomes $1:1$. How much juice is added, and what fraction of the final drink is juice?
6 marks
Mark scheme
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Answer. $3:4$
- Divide both parts by $6$.
- $3:4$
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Answer. £$8$ and £$32$
- There are $5$ parts, so one part is £$8$.
- £$8$ and £$32$
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Answer. £$20$, £$30$ and £$40$
- There are $9$ parts, so one part is £$10$.
- £$20$, £$30$ and £$40$
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Answer. $40$ girls, and $64$ students
- One part is $24 \div 3 = 8$.
- Girls $= 5 \times 8 = 40$, so the total is $64$.
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Answer. $2$ km
- $8 \times 25000 = 200000$ cm.
- $200000$ cm $= 2000$ m $= 2$ km.
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Answer. $6$ litres of red, and $15$ litres of blue
- $15 \div 5 \times 2 = 6$ litres of red.
- There are $7$ parts in $21$ litres, so the blue is $\dfrac{5}{7} \times 21 = 15$ litres.
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Answer. Amy £$48$, Ben £$60$
- The difference is $1$ part, so one part is £$12$.
- Amy receives $4 \times 12 = £48$.
- Ben receives $5 \times 12 = £60$.
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Answer. $450$ ml of water. Add $270$ ml of juice. The final drink is half juice.
- Water $= \dfrac{180}{2} \times 5 = 450$ ml.
- The juice must also become $450$ ml, so add $270$ ml.
- The final ratio is $1:1$, so half of the drink is juice.