Podcast
Questions and Answers
How many bottles will the machine fill in five hours if it fills 840 bottles in six hours?
How many bottles will the machine fill in five hours if it fills 840 bottles in six hours?
How much red pigment is needed if 1 part requires 75 mL of base and you have 1800 mL of base?
How much red pigment is needed if 1 part requires 75 mL of base and you have 1800 mL of base?
If the scale of Rashmi's map is 1 cm representing 18 km, what distance does she drive on the map for a road journey of 72 km?
If the scale of Rashmi's map is 1 cm representing 18 km, what distance does she drive on the map for a road journey of 72 km?
Given that 2 kg of sugar contains $9 \times 10^6$ sugar crystals, how many crystals are there in 1.2 kg of sugar?
Given that 2 kg of sugar contains $9 \times 10^6$ sugar crystals, how many crystals are there in 1.2 kg of sugar?
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If a bacteria photograph is enlarged 20,000 times, what would be its enlarged length if the actual length of the bacteria is 0.0001 m?
If a bacteria photograph is enlarged 20,000 times, what would be its enlarged length if the actual length of the bacteria is 0.0001 m?
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Are the parking charges at the railway station directly proportional to the parking time?
Are the parking charges at the railway station directly proportional to the parking time?
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Study Notes
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.
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Description
This quiz covers various mathematical concepts related to proportions, mixtures, and measurements. Topics include parking charges, paint mixture ratios, production rates, and calculations involving bacterial enlargement and model dimensions. Test your understanding of how to apply proportions in practical scenarios.
