Rates & Ratios

5.1 Rate per 1 000

Rate per 1 000 = (Count ÷ Population) × 1 000

Example: 4 200 births in a city of 280 000. Birth rate = (4 200 ÷ 280 000) × 1 000 = 15 per 1 000.

5.2 Ratio problems

If A : B = m : n, then A = m/(m+n) × Total
                       B = n/(m+n) × Total

Example: staff split in ratio 3:2 between departments A and B, 150 total. A = 3/5 × 150 = 90. B = 2/5 × 150 = 60.

5.3 Proportional scaling

New value = Old value × (New base ÷ Old base)

5.4 Inverse proportion

Total work (worker-days) = Workers × Days = constant
New days = Total work ÷ New workers

Example: 10 workers complete a task in 18 days. Total work = 180 worker-days. With 15 workers: 180 ÷ 15 = 12 days.

5.5 Carbon tax chain problems

CO2 (tonnes) = Fuel (litres) × CO2 factor (kg/L) ÷ 1 000
Tax (€)       = CO2 (tonnes) × tax rate (€/tonne)

Example: 2 000 000 litres/year, factor 2.54 kg/L, tax €38/tonne. CO2 = 5 080 tonnes. Tax = €193 040.