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Ratio, percentage, money and rates

Share in a ratio by dividing into parts; direct and inverse proportion (y = kx, y = k/x).

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Ratio and proportion

Share in a ratio by dividing into parts; direct and inverse proportion (y = kx, y = k/x).

Worked example: Share US$180 in the ratio 2 : 3 : 4.

9 parts → 1 part = 20 → US$40, US$60, US$80

Percentages

Percentage increase and decrease; reverse percentages; simple and compound interest.

Worked example: After a 15% increase a price is US$92. Find the original price.

1.15x = 92 → x = US$80

Worked example: US$2 000 is invested at 5% compound interest per year. Find its value after 3 years.

2 000 × 1.05³ = US$2 315.25

Rates

Speed = distance ÷ time; density; rates of pay; best-buy comparisons; exchange rates and time (24-hour clock, time zones).

Exam tip: For reverse percentages, divide by the multiplier – never take the percentage of the new value.

Check yourself

  1. Increase 250 by 12%.
  2. A car travels 150 km in 2 h 30 min. Find its average speed.
  3. Find the simple interest on US$500 at 4% for 3 years.
Show answers
  1. 280
  2. 60 km/h
  3. US$60
Next topicAlgebraic manipulation

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