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Exam questions · Maths · Ratio and Proportion

Ratio: Simplifying and Sharing

  • 6 exam questions
  • 18 marks
  • 9 quick checks
  1. 1 Write [2 marks]

    Write the ratio \(60 : 45\) in its simplest form.

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    Model answer

    The highest common factor of 60 and 45 is 15, so \(60 : 45 = 4 : 3\).

    Mark scheme

    • Divides both by a common factor, such as \(20 : 15\) or \(12 : 9\) — M1
    • \(4 : 3\) — A1
  2. 2 Calculate [3 marks]

    \(\pounds 90\) is shared in the ratio \(2 : 7\). Calculate the larger share.

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    Model answer

    There are \(2 + 7 = 9\) parts, and one part is \(90 \div 9 = 10\). The larger share is \(7 \times 10 = \pounds 70\).

    Mark scheme

    • \(2 + 7 = 9\) or \(90 \div 9\) — M1
    • \(7 \times 10\) — M1
    • \(\pounds 70\) — A1
  3. 3 Calculate [3 marks]

    A fruit drink is made from orange juice, mango juice and pineapple juice in the ratio \(3 : 2 : 1\). A bottle holds 1.2 litres of the drink. Calculate the volume of mango juice in the bottle. Give your answer in millilitres.

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    Model answer

    There are \(3 + 2 + 1 = 6\) parts. \(1.2\text{ litres} = 1200\) ml, so one part is \(1200 \div 6 = 200\) ml. The mango juice is \(2 \times 200 = 400\) ml.

    Mark scheme

    • \(1200 \div 6 = 200\) — M1
    • \(2 \times 200\) — M1
    • 400 ml — A1
  4. 4 Calculate [3 marks]

    At a concert the ratio of adults to children is \(3 : 7\). There are 80 more children than adults. Calculate the total number of people at the concert.

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    Model answer

    The difference is \(7 - 3 = 4\) parts, and 4 parts \(= 80\), so one part is 20. The total is \(10 \times 20 = 200\).

    Mark scheme

    • \(80 \div 4 = 20\) — M1
    • \(10 \times 20\) or \(60 + 140\) — M1
    • 200 — A1
  5. 5 Calculate [3 marks]

    The ages of Sam and Tom are in the ratio \(4 : 5\). The sum of their ages is 36 years. Calculate Tom's age.

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    Model answer

    There are \(4 + 5 = 9\) parts, so one part is \(36 \div 9 = 4\) years. Tom is \(5 \times 4 = 20\) years old.

    Mark scheme

    • \(36 \div 9 = 4\) — M1
    • \(5 \times 4\) — M1
    • 20 — A1
  6. 6 Find [4 marks]

    \(a : b = 5 : 2\) and \(b : c = 3 : 4\). (a) Find \(a : b : c\). [2 marks] (b) \(a + b + c = 87\). Calculate the value of \(c\). [2 marks]

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    Model answer

    (a) Make \(b\) the same in both ratios, using the lowest common multiple of 2 and 3, which is 6. Then \(a : b = 15 : 6\) and \(b : c = 6 : 8\), so \(a : b : c = 15 : 6 : 8\). (b) There are \(15 + 6 + 8 = 29\) parts, so one part is \(87 \div 29 = 3\) and \(c = 8 \times 3 = 24\).

    Mark scheme

    • (a) \(15 : 6\) or \(6 : 8\) seen — M1
    • (a) \(15 : 6 : 8\) — A1
    • (b) \(87 \div 29 = 3\) — M1
    • (b) 24 — A1

Quick check

  1. 1

    Simplify the ratio \(24 : 36\).

    1. A\(4 : 6\)
    2. B\(2 : 3\)
    3. C\(3 : 2\)
    4. D\(6 : 9\)
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    B: \(2 : 3\)

    The highest common factor of 24 and 36 is 12. Dividing both parts by 12 gives \(2 : 3\).

  2. 2

    Which ratio is equivalent to \(3 : 5\)?

    1. A\(9 : 15\)
    2. B\(9 : 12\)
    3. C\(6 : 8\)
    4. D\(5 : 3\)
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    A: \(9 : 15\)

    Multiplying both parts of \(3 : 5\) by 3 gives \(9 : 15\). The others do not keep the same relationship.

  3. 3

    Write \(40\) cm to \(1.2\) m as a ratio in its simplest form.

    1. A\(40 : 1.2\)
    2. B\(1 : 30\)
    3. C\(3 : 1\)
    4. D\(1 : 3\)
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    D: \(1 : 3\)

    Change to the same unit: \(1.2\) m \(= 120\) cm. Then \(40 : 120 = 1 : 3\).

  4. 4

    \(\pounds 60\) is shared in the ratio \(2 : 3\). How much is the larger share?

    1. A\(\pounds 24\)
    2. B\(\pounds 30\)
    3. C\(\pounds 36\)
    4. D\(\pounds 40\)
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    C: \(\pounds 36\)

    There are \(2 + 3 = 5\) parts, and one part is \(60 \div 5 = 12\). The larger share is \(3 \times 12 = 36\).

  5. 5

    The ratio of boys to girls in a class is \(3 : 5\). There are 12 boys. How many girls are there?

    1. A15
    2. B20
    3. C36
    4. D4
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    B: 20

    One part is \(12 \div 3 = 4\), so the number of girls is \(5 \times 4 = 20\).

  6. 6

    Red and blue beads are in the ratio \(2 : 5\). What fraction of the beads are red?

    1. A\(\dfrac{2}{7}\)
    2. B\(\dfrac{2}{5}\)
    3. C\(\dfrac{5}{7}\)
    4. D\(\dfrac{2}{3}\)
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    A: \(\dfrac{2}{7}\)

    The whole is \(2 + 5 = 7\) parts, so red is \(\dfrac{2}{7}\).

  7. 7

    Orange juice and water are mixed in the ratio \(1 : 4\). There is 250 ml of orange juice. How much water is there?

    1. A750 ml
    2. B1250 ml
    3. C4 ml
    4. D1000 ml
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    D: 1000 ml

    The water is 4 times the juice, so \(4 \times 250 = 1000\) ml.

  8. 8

    Amy and Ben share money in the ratio \(3 : 7\). Ben gets \(\pounds 20\) more than Amy. How much money is shared?

    1. A\(\pounds 35\)
    2. B\(\pounds 80\)
    3. C\(\pounds 50\)
    4. D\(\pounds 20\)
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    C: \(\pounds 50\)

    The difference is \(7 - 3 = 4\) parts, so 4 parts \(= 20\) and one part is 5. The total is \(10 \times 5 = 50\).

  9. 9

    \(A : B = 2 : 3\) and \(B : C = 4 : 5\). Write \(A : B : C\) in its simplest form.

    1. A\(2 : 3 : 5\)
    2. B\(8 : 12 : 15\)
    3. C\(8 : 12 : 20\)
    4. D\(6 : 12 : 15\)
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    B: \(8 : 12 : 15\)

    Make the \(B\) values match. The lowest common multiple of 3 and 4 is 12. Then \(A : B = 8 : 12\) and \(B : C = 12 : 15\), so \(A : B : C = 8 : 12 : 15\).