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The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?
- a)20 ft
- b)25 ft
- c)750 ft
- d)900 ft
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The circumference of the front wheel of a cart is 30 ft long and that ...
The circumference of the front wheel is 30 ft and that of the rear wheel is 36 feet.
Let the rear wheel make n revolutions. At this time, the front wheel should have made n+5 revolutions.
As both the wheels would have covered the same distance, n*36 = (n+5)*30
36n = 30n + 150
6n = 150
n = 25.
Distance covered = 25*36 = 900 ft.
Let the rear wheel make n revolutions. At this time, the front wheel should have made n+5 revolutions.
As both the wheels would have covered the same distance, n*36 = (n+5)*30
36n = 30n + 150
6n = 150
n = 25.
Distance covered = 25*36 = 900 ft.
Most Upvoted Answer
The circumference of the front wheel of a cart is 30 ft long and that ...
Understanding the Problem
To determine the distance traveled by the cart, we need to analyze the revolutions of the front and back wheels.
Wheel Circumference
- Front Wheel: 30 ft
- Back Wheel: 36 ft
Revolutions of Wheels
Let the number of revolutions made by the back wheel be \( x \).
Then, the front wheel has done \( x + 5 \) revolutions.
Distance Traveled Calculation
The distance traveled by each wheel can be calculated using the formula:
- Distance = Circumference × Number of Revolutions
For the back wheel:
- Distance (Back Wheel) = 36 ft × \( x \) = \( 36x \) ft
For the front wheel:
- Distance (Front Wheel) = 30 ft × \( (x + 5) \) = \( 30(x + 5) \) ft
Setting Distances Equal
Since the cart travels the same distance regardless of which wheel is considered, we set the distances equal:
\[ 36x = 30(x + 5) \]
Expanding the equation:
- \( 36x = 30x + 150 \)
Simplifying:
- \( 36x - 30x = 150 \)
- \( 6x = 150 \)
- \( x = 25 \)
Calculating Distance
Now, substituting \( x \) back into either distance equation:
Distance traveled by the back wheel:
- \( 36x = 36 \times 25 = 900 \) ft
Conclusion
Thus, the total distance traveled by the cart when the front wheel has done five more revolutions than the rear wheel is 900 ft. Therefore, the correct answer is option D.
To determine the distance traveled by the cart, we need to analyze the revolutions of the front and back wheels.
Wheel Circumference
- Front Wheel: 30 ft
- Back Wheel: 36 ft
Revolutions of Wheels
Let the number of revolutions made by the back wheel be \( x \).
Then, the front wheel has done \( x + 5 \) revolutions.
Distance Traveled Calculation
The distance traveled by each wheel can be calculated using the formula:
- Distance = Circumference × Number of Revolutions
For the back wheel:
- Distance (Back Wheel) = 36 ft × \( x \) = \( 36x \) ft
For the front wheel:
- Distance (Front Wheel) = 30 ft × \( (x + 5) \) = \( 30(x + 5) \) ft
Setting Distances Equal
Since the cart travels the same distance regardless of which wheel is considered, we set the distances equal:
\[ 36x = 30(x + 5) \]
Expanding the equation:
- \( 36x = 30x + 150 \)
Simplifying:
- \( 36x - 30x = 150 \)
- \( 6x = 150 \)
- \( x = 25 \)
Calculating Distance
Now, substituting \( x \) back into either distance equation:
Distance traveled by the back wheel:
- \( 36x = 36 \times 25 = 900 \) ft
Conclusion
Thus, the total distance traveled by the cart when the front wheel has done five more revolutions than the rear wheel is 900 ft. Therefore, the correct answer is option D.
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The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?a)20 ftb)25 ftc)750 ftd)900 ftCorrect answer is option 'D'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?a)20 ftb)25 ftc)750 ftd)900 ftCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?a)20 ftb)25 ftc)750 ftd)900 ftCorrect answer is option 'D'. Can you explain this answer?.
The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?a)20 ftb)25 ftc)750 ftd)900 ftCorrect answer is option 'D'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?a)20 ftb)25 ftc)750 ftd)900 ftCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 36 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?a)20 ftb)25 ftc)750 ftd)900 ftCorrect answer is option 'D'. Can you explain this answer?.
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