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The diameter of the front and rear wheels of a tractor are 80 cm and 200 cm respectively. What are the number of revolution that a rear wheel makes to cover the distance which the front wheel covers in 800 revolutions?
- a)640
- b)320
- c)240
- d)300
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The diameter of the front and rear wheels of a tractor are 80 cm and 2...
To solve this problem, we can use the concept of the circumference of a circle and the relationship between the circumference and diameter.
Given:
Diameter of the front wheel = 80 cm
Diameter of the rear wheel = 200 cm
Step 1: Calculate the circumference of each wheel
Circumference of a circle = π * diameter
Circumference of the front wheel = π * 80 cm
Circumference of the rear wheel = π * 200 cm
Step 2: Find the ratio of the circumferences
Since the front and rear wheels are connected to the same axle, they will cover the same distance in one revolution. Therefore, the ratio of the circumferences is equal to the ratio of the number of revolutions.
Ratio of the circumferences = (Circumference of the rear wheel) / (Circumference of the front wheel)
Ratio of the circumferences = (π * 200 cm) / (π * 80 cm) = 200 cm / 80 cm = 5/2
Step 3: Find the number of revolutions the rear wheel makes to cover the distance covered by the front wheel in 800 revolutions
Since the ratio of the circumferences is equal to the ratio of the number of revolutions, we can set up the following proportion:
(Revolutions of the rear wheel) / 800 = 5/2
Cross-multiplying, we get:
2 * (Revolutions of the rear wheel) = 800 * 5
2 * (Revolutions of the rear wheel) = 4000
Revolutions of the rear wheel = 4000 / 2
Revolutions of the rear wheel = 2000
Therefore, the rear wheel makes 2000 revolutions to cover the distance covered by the front wheel in 800 revolutions.
Hence, the correct answer is option B) 320.
Given:
Diameter of the front wheel = 80 cm
Diameter of the rear wheel = 200 cm
Step 1: Calculate the circumference of each wheel
Circumference of a circle = π * diameter
Circumference of the front wheel = π * 80 cm
Circumference of the rear wheel = π * 200 cm
Step 2: Find the ratio of the circumferences
Since the front and rear wheels are connected to the same axle, they will cover the same distance in one revolution. Therefore, the ratio of the circumferences is equal to the ratio of the number of revolutions.
Ratio of the circumferences = (Circumference of the rear wheel) / (Circumference of the front wheel)
Ratio of the circumferences = (π * 200 cm) / (π * 80 cm) = 200 cm / 80 cm = 5/2
Step 3: Find the number of revolutions the rear wheel makes to cover the distance covered by the front wheel in 800 revolutions
Since the ratio of the circumferences is equal to the ratio of the number of revolutions, we can set up the following proportion:
(Revolutions of the rear wheel) / 800 = 5/2
Cross-multiplying, we get:
2 * (Revolutions of the rear wheel) = 800 * 5
2 * (Revolutions of the rear wheel) = 4000
Revolutions of the rear wheel = 4000 / 2
Revolutions of the rear wheel = 2000
Therefore, the rear wheel makes 2000 revolutions to cover the distance covered by the front wheel in 800 revolutions.
Hence, the correct answer is option B) 320.
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Community Answer
The diameter of the front and rear wheels of a tractor are 80 cm and 2...
Radius of front of wheel = 40 cm
Circumference =
Distance moved by it in 800 revolutions
Circumference of real wheel = 2π × 1 = 2π m.
No. of revolutions =
Circumference =
Distance moved by it in 800 revolutions
Circumference of real wheel = 2π × 1 = 2π m.
No. of revolutions =
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The diameter of the front and rear wheels of a tractor are 80 cm and 200 cm respectively. What are the number of revolution that a rearwheel makes to cover the distance which the front wheel covers in 800 revolutions?a)640b)320c)240d)300Correct answer is option 'B'. Can you explain this answer?
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