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0580/32 Oct/Nov 2023, Question 7: Dividing in a Given Ratio

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 16 marks

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The question, in short

Elize, Lily and Marco invest $5000, $8000 and $3000 and share a $40 000 profit in investment ratio; also work with ribbon probabilities, a 120 m length bound, frame costs in dollars and euros, shaded area and percentage profit.

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

Part (a) · 3 marks

Share $40 000 among the three investors in the ratio of their investments; find each person's amount.

  1. 15000 : 8000 : 3000 = 5 : 8 : 3, total 16 parts
  2. 2One part = 40 000 ÷ 16 = 2500
  3. 3Elize 5 × 2500 = 12500, Lily 8 × 2500 = 20000, Marco 3 × 2500 = 7500

Answer12500, 20000, 7500

Part (bia) · 1 mark

With 20 rolls (8 red, 6 blue, 4 yellow, 2 pink), mark the probability of choosing yellow on the scale.

  1. 1P(yellow) = 4/20 = 0.2: arrow at 0.2

AnswerArrow at 0.2

Part (bib) · 1 mark

Mark on the probability scale the chance that a randomly chosen roll is not red.

  1. 1P(not red) = 12/20 = 0.6: arrow at 0.6

AnswerArrow at 0.6

Part (bic) · 1 mark

Mark on the probability scale the probability that a randomly chosen roll is green.

  1. 1There are no green rolls, P(green) = 0: arrow at 0

AnswerArrow at 0

Part (bii) · 2 marks

Given l = 120 m to the nearest metre, complete the lower and upper bounds for l.

  1. 1Half a metre either side of 120
  2. 2119.5 ≤ l < 120.5

Answer119.5 ≤ l < 120.5

Part (c) · 3 marks

Compare a $5.80 New York frame with a 4.50 euro Paris frame at 1 euro = $1.37; find the cost difference in euros to 2 decimal places.

  1. 1New York price in euros = 5.80 ÷ 1.37 = 4.233… euros
  2. 2Difference = 4.50 − 4.233… = 0.266…
  3. 3≈ 0.27 euros

Answer0.27

Part (di) · 3 marks

A circle of diameter 18 cm sits inside a square of side 18 cm; calculate the shaded area between them.

  1. 1Square = 18² = 324
  2. 2Circle = π × 9² = 81π = 254.4…
  3. 3Shaded = 324 − 254.4… = 69.53… ≈ 69.5 cm²

Answer69.5 or 69.49 to 69.531

Part (dii) · 2 marks

A picture bought for $12.50 is sold for $20.25; calculate the percentage profit.

  1. 1Profit = 20.25 − 12.50 = 7.75
  2. 27.75/12.50 × 100 = 62%

Answer62

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Also searched as: 0580/32/O/N/23 · 0580_w23_qp_32 · 0580 w23 32 · question 7.
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