[discia] GCSE Maths › Ratio and Proportion › Ratio

Ratio

discia.org 10 questions · 31 marks
Name Date
  1. Either paper 1 mark

    Anya is asked to share 96 stickers between Owen and Priya in the ratio \(2 : 6\).

    She writes:

    Owen gets \(96 \times 2 = 192\) stickers

    Priya gets \(96 \times 6 = 576\) stickers

    Describe what Anya has done wrong.

    Show answer
    Anya multiplied the total by each ratio number, instead of first dividing by the total number of parts to find the value of one part. The correct shares are Owen 24 and Priya 72 stickers.
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  2. Either paper 3 marks

    Marcus makes green paint by mixing blue paint and yellow paint.

    The graph shows how much of each colour of paint to use.

    yellow paint (litres)blue paint (litres)510152051015200
    (a)

    Marcus uses 8 litres of yellow paint.

    State how much blue paint Marcus uses.

    (b)

    Marcus now uses 36 litres of yellow paint.

    How much green paint does he make?

    Show answer
    (a) \(6\ \text{litres}\)
    (b) \(63\ \text{litres}\)
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  3. Either paper 2 marks

    In a bag, the number of green discs : the number of blue discs = \(13 : 8\)

    Each statement below is about the discs in the bag.

    (a)

    "In total there are 21 discs."

    Tick one box: true, false or cannot tell.

    (b)

    "There are more green discs than blue discs."

    Tick one box: true, false or cannot tell.

    Show answer
    (a) Cannot tell. This total is in the list of possible totals, so it could be right, but the ratio does not make it certain.
    (b) True. The colour named has the larger part of the ratio, so it has more discs in every possible bag.
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  4. Either paper 2 marks

    There are 140 counters in a bag. There are only red counters and blue counters in the bag.

    number of red counters : number of blue counters = \(1 : 4\)

    Noah has to work out how many red counters are in the bag.

    Noah says, "There are 28 red counters in the bag, because 1 is \(\frac{1}{5}\) of 5 and 28 is \(\frac{1}{5}\) of 140."

    Is Noah correct? You must give a reason for your answer.

    Show answer
    Yes. There are 28 red counters (140 ÷ 5 × 1). Noah compared the red share with all the parts in the bag, which is the whole.
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  5. Either paper 3 marks

    The diagram shows two angles.

    The angles are in the ratio \(1 : 9\).

    Show that the smaller angle is \(36^\circ\). Give the angle fact that tells you the total of the two angles.

    Show answer
    Angles around a point add up to 360°, so the total is \(360^\circ\). One part is \(360 \div 10 = 36^\circ\), and \(1 \times 36 = 36^\circ\), which is the smaller angle
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  6. Either paper 5 marks

    Amy and Ben share 70 counters in the ratio \(3 : 7\).

    (a)

    Calculate how many counters Ben gets.

    (b)

    Ben then gives 11 of his counters to Amy.

    Work out the new ratio of Amy's counters to Ben's counters. Give your answer in its simplest form.

    Show answer
    (a) \(49\)
    (b) \(16 : 19\)
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  7. Either paper 4 marks

    Callum and Aisha share some money in the ratio \(5 : 7\).

    Callum gets £60.

    (a)

    Work out how much money Aisha gets.

    (b)

    Work out how much money they shared altogether.

    Show answer
    (a) \(\text{£}84\)
    (b) \(\text{£}144\)
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  8. Either paper 5 marks

    Grace, Harry and Isla share £340 in the ratio \(4 : 6 : 7\).

    (a)

    Calculate how much money Isla gets.

    (b)

    Calculate how much more money Isla gets than Grace.

    Show answer
    (a) \(\text{£}140\)
    (b) \(\text{£}60\)
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  9. Either paper 4 marks

    The three angles of a triangle are in the ratio \(9 : 17 : 19\).

    (a)

    Work out the size of each of the three angles.

    (b)

    Write down whether the triangle is acute-angled, right-angled or obtuse-angled.

    Show answer
    (a) \(36^\circ\), \(68^\circ\) and \(76^\circ\)
    (b) acute-angled
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  10. Either paper 2 marks

    Sam and Priya throw darts at a target.

    Sam's ratio of hits to misses is \(5 : 2\)

    Priya's ratio of hits to misses is \(6 : 1\)

    Priya says that because 6 is bigger than 5, she must have more hits than Sam.

    Give an example to show that this might not be true.

    Show answer
    e.g. Priya: 6 hits, 1 miss (\(6 : 1\)). Sam: 30 hits, 12 misses (\(5 : 2\) scaled up). Sam has more hits than Priya, even though 5 is smaller than 6.
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discia.org Ratio · sheet 1
Answers Ratio · sheet 1
  1. Anya multiplied the total by each ratio number, instead of first dividing by the total number of parts to find the value of one part. The correct shares are Owen 24 and Priya 72 stickers.
  2. (a) \(6\ \text{litres}\)
    (b) \(63\ \text{litres}\)
  3. (a) Cannot tell. This total is in the list of possible totals, so it could be right, but the ratio does not make it certain.
    (b) True. The colour named has the larger part of the ratio, so it has more discs in every possible bag.
  4. Yes. There are 28 red counters (140 ÷ 5 × 1). Noah compared the red share with all the parts in the bag, which is the whole.
  5. Angles around a point add up to 360°, so the total is \(360^\circ\). One part is \(360 \div 10 = 36^\circ\), and \(1 \times 36 = 36^\circ\), which is the smaller angle
  6. (a) \(49\)
    (b) \(16 : 19\)
  7. (a) \(\text{£}84\)
    (b) \(\text{£}144\)
  8. (a) \(\text{£}140\)
    (b) \(\text{£}60\)
  9. (a) \(36^\circ\), \(68^\circ\) and \(76^\circ\)
    (b) acute-angled
  10. e.g. Priya: 6 hits, 1 miss (\(6 : 1\)). Sam: 30 hits, 12 misses (\(5 : 2\) scaled up). Sam has more hits than Priya, even though 5 is smaller than 6.
discia.org Ratio · sheet 1