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0580/32 Feb/Mar 2021, Question 2: Calculating a Percentage of a Quantity

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 13 marks

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The question, in short

Ski holiday problem set covering room occupancy percentage, mountain temperatures, equipment hire costs from a table, lift passenger totals, currency comparison of pass prices, and an error interval for a rounded height.

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

Part (a) · 1 mark

Find what percentage of the hotel's 840 rooms are occupied when 735 are taken.

  1. 1735 ÷ 840 × 100 = 87.5%

Answer87.5

Part (b) · 2 marks

Given hotel temperature 21 °C, 26.7 °C above the summit, and summit 3.2 °C below the base, find the base temperature.

  1. 1Top of mountain = 21 − 26.7 = −5.7 °C
  2. 2Bottom = −5.7 + 3.2 = −2.5 °C

Answer−2.5

Part (c) · 2 marks

Using the hire table, total the cost for two adults skiing 7 days, one child skiing 3 days and snowboarding 4 days, plus three 7-day helmets.

  1. 1Adults: 2 × 128.00 + 2 × 20.70 = 297.40
  2. 2Child: 47.60 + 70.20 + 16.70 = 134.50
  3. 3Total = 297.40 + 134.50 = $431.90

Answer431.90

Part (d) · 3 marks

A lift holds 4000 per hour, runs 10 hours; find total passengers when 90% full for 3 hours and 75% full for 7 hours.

  1. 190% full for 3 hours: 3 × 0.9 × 4000 = 10 800
  2. 275% full for 7 hours: 7 × 0.75 × 4000 = 21 000
  3. 3Total = 10 800 + 21 000 = 31 800 passengers

Answer31 800

Part (e) · 3 marks

Passes cost 51400 rupees prepaid or $684 at 1 rupee = $0.0129; show the saving is 1620 rupees to the nearest 10.

  1. 1Cost in America in rupees = 684 ÷ 0.0129 = 53 023.25…
  2. 2Saving = 53 023.25… − 51 400 = 1623.25…
  3. 3Saving ≈ 1623 rupees, which is 1620 correct to the nearest 10

Answer1623

Part (f) · 2 marks

The height h = 2642 m is rounded to the nearest metre; complete the inequality giving the lower and upper bounds for h.

  1. 1Nearest metre: half a metre either side
  2. 22642 − 0.5 = 2641.5 and 2642 + 0.5 = 2642.5
  3. 32641.5 ≤ h < 2642.5

Answer2641.5 2642.5

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