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0580/42 May/Jun 2024, Question 1: Dividing in a Given Ratio

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 12 marks

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The question, in short

Fruit drink problem: simplify a juice ratio, share one litre by a ratio, find a selling price after 15% profit, project exponential growth at 2.5% over 5 years, and find a lower bound for gap d.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 2 marks

Write the ratio of apple juice to mango juice in simplest form, using 1.5 litres and 450 millilitres.

  1. 11.5 litres = 1500 ml
  2. 21500 : 450 = 10 : 3

Answer10 : 3

Part (b) · 3 marks

Share one litre between three cups in the ratio 9 : 6 : 10, giving each amount in millilitres.

  1. 19 + 6 + 10 = 25 parts, 1000 ÷ 25 = 40 ml per part
  2. 29 × 40 = 360 ml, 6 × 40 = 240 ml, 10 × 40 = 400 ml

Answer360 ml, 240 ml, 400 ml

Part (c) · 2 marks

Find the selling price of a bottle bought for $3.20 and sold at 15% profit.

  1. 1A 15% profit means selling at 115% of the cost.
  2. 2Selling price = 3.20 × 1.15 = 3.68

Answer3.68

Part (d) · 2 marks

Find bottles sold this year, given 16 620 five years ago and 2.5% annual exponential growth.

  1. 1Growing 2.5% a year means × 1.025 each year.
  2. 2After 5 years: 16 620 × 1.025⁵
  3. 3= 18804.0…

Answer18804.0…

Part (e) · 3 marks

Using 18.5 cm and 23 cm each correct to the nearest unit, find the lower bound of gap d.

  1. 1Lower bound of shelf gap = 23 − 0.5 = 22.5 cm
  2. 2Upper bound of bottle = 18.5 + 0.05 = 18.55 cm
  3. 3d = 22.5 − 18.55 = 3.95 cm

Answer3.95

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Also searched as: 0580/42/M/J/24 · 0580_s24_qp_42 · 0580 s24 42 · question 1.
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