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4024/21 May/Jun 2020, Question 5: Profit and Loss

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 14 marks

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The question, in short

Triangular prism chocolate box with right-angled triangular end (sides x cm, 6 cm, hypotenuse 7.5 cm) and length 14 cm; solve parts on finding x, carton height, carton counts, production cost, and shop profit.

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

Part (a) · 2 marks

Use Pythagoras on the right-angled triangular end with sides x and 6 and hypotenuse 7.5 to show x = 4.5.

  1. 16² + x² = 7.5²
  2. 2x² = 56.25 − 36 = 20.25
  3. 3x = √20.25 = 4.5

Answer√(7.5² − 6²) = 4.5

Part (bi) · 3 marks

Carton 30 cm by 28 cm by h cm holds 80 boxes exactly; calculate h.

  1. 1Volume of one box = 1/2 × 4.5 × 6 × 14 = 189 cm³
  2. 280 boxes: 80 × 189 = 15 120 cm³
  3. 330 × 28 × h = 15 120
  4. 4h = 15 120 ÷ 840 = 18

Answer18

Part (bii) · 2 marks

With 37 500 boxes packed into cartons, find how many complete cartons are filled.

  1. 137 500 ÷ 80 = 468.75
  2. 2468 complete cartons

Answer468

Part (ci) · 2 marks

Bars sell at $0.70 with 40% profit; work out the company's production cost per bar.

  1. 1$0.70 is 140% of the cost
  2. 2Cost = 0.70 × 100/140 = $0.50

Answer0.50

Part (cii) · 5 marks

Shop buys a carton of 80 bars; sells 3/5 at 30% profit and the rest at $0.84 each; find overall percentage profit.

  1. 13/5 × 80 = 48 bars sold at 0.70 × 1.30 = $0.91: 48 × 0.91 = $43.68
  2. 280 − 48 = 32 bars at $0.84: 32 × 0.84 = $26.88
  3. 3Total income = 43.68 + 26.88 = $70.56; cost = 80 × 0.70 = $56
  4. 4Profit = 70.56 − 56 = $14.56
  5. 5Percentage profit = 14.56/56 × 100 = 26%

Answer26

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