Mathematical Proportions and Calculations

Car Parking Charges

• Parking charges are not in direct proportion to parking time.
• Different time slots have different fees.
  • Up to 4 hours: 60
  • 8 hours: 100
  • 12 hours: 140
  • 24 hours: 180

Paint Mixture Proportions

• A paint mixture uses a ratio of 1 part red pigment to 8 parts base.
• Parts of red pigment | Parts of base
  • 1 | 8
  • 4 | 32
  • 7 | 56
  • 12 | 96
  • 20 | 160

Paint Mixture Calculation

• If 1 part of red pigment requires 75 mL of base, to use 1800 mL base, one would need 24 parts of red pigment.

Machine Production Rate

• A machine fills 140 bottles per hour.
• In five hours, the machine will fill 700 bottles.
• A machine in a soft drink factory fills 840 bottles in six hours. This means it fills 840/6 = 140 bottles per hour. In five hours, it will fill 140 bottles/hour * 5 hours = 700 bottles.

Bacteria Enlargement

• Actual bacteria length is 10^-7 cm.
• Enlarged length at 20,000x is 2.5 cm.
• A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. This means the actual length of the bacteria is 5 cm / 50,000 = 10^-7 cm.
• If the photograph is enlarged 20,000 times, its enlarged length would be (10^-7 cm * 20,000) = 2×10−3 cm = 0.002 cm

Model Ship Dimensions

• Model ship mast is 9 cm high, actual ship mast is 12 m high, scale is 1/1333.33.
• If actual ship length is 28 m, model ship length is 21 cm.

Sugar Crystals Calculation

• 2 kg of sugar contains 9 × 10^6 crystals.
  • 5 kg of sugar would contain 2.25 × 10^7 crystals.
  • 1.2 kg of sugar would contain 5.4 × 10^6 crystals.

Road Map Scale

• Map scale is 1 cm : 18 km.
• 72 km distance on road would correspond to 4 cm on map.

Pole Shadow Length and Height

• A 5.6 m pole casts a 3.2 m shadow.
  • A 10.5 m pole would cast a 6 m shadow.
  • A 5 m shadow corresponds to a pole of 8.75 m.