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Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?
Correct answer is '75'. Can you explain this answer?
Verified Answer
Samrat covers the total journey of 810 km to his village partly by tra...
Let the speed of the bus be b km/hr
The speed of the train = 12b km/hr
Let the bus normally travel for 3x hours and let the train normally travel for 2x hours.
3xb + 2.4xb = 810
xb = 150
If the train travels for the number of hours that the bus travels,
The speed of the train = 12b km/hr
Let the bus normally travel for 3x hours and let the train normally travel for 2x hours.
3xb + 2.4xb = 810
xb = 150
If the train travels for the number of hours that the bus travels,
5.6xb - 810 = 0.4b
5.6(150) -810 = 0.4b
b = 75
The speed of the bus = 75 km/hr
Answer: 75
Most Upvoted Answer
Samrat covers the total journey of 810 km to his village partly by tra...
Given:
- Total distance of the journey = 810 km
- Train is 20% faster than the bus
- If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes
- The normal travelling hours of bus and train are in the ratio 3:2
To find:
- Speed of the bus in km/hr
Assumptions:
- Let the speed of the bus be x km/hr
- The speed of the train is 20% faster than the bus, so the speed of the train is (1 + 20/100) * x = 1.2x km/hr
Calculations:
Let the normal travelling time of the bus be 3t hours and the normal travelling time of the train be 2t hours.
- Distance travelled by the bus in 3t hours = x * 3t
- Distance travelled by the train in 2t hours = 1.2x * 2t
According to the given condition, if the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes.
- New travelling time of the bus = 3t - 24/60 hours
- New travelling time of the train = 2t - 24/60 hours
As the distance covered by both the bus and train remains the same, we can equate the distances:
- x * (3t - 24/60) = 1.2x * (2t - 24/60)
Simplifying the equation:
- 3t - 24/60 = (1.2 * 2t) - 24/60
- 3t - 24/60 = 2.4t - 24/60
- 0.6t = 24/60
- t = (24/60) / 0.6
- t = 24/60 * 10/6
- t = 4/10 * 10/6
- t = 2/3
Therefore, the normal travelling time of the bus, 3t = 3 * (2/3) = 2 hours.
Speed of the bus:
To find the speed of the bus, we can use the formula: Speed = Distance / Time
- Speed of the bus = (Distance travelled by the bus) / (Normal travelling time of the bus)
- Speed of the bus = (x * 3t) / (3t)
- Speed of the bus = x km/hr
Therefore, the speed of the bus is x km/hr.
Conclusion:
The speed of the bus is 75 km/hr.
- Total distance of the journey = 810 km
- Train is 20% faster than the bus
- If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes
- The normal travelling hours of bus and train are in the ratio 3:2
To find:
- Speed of the bus in km/hr
Assumptions:
- Let the speed of the bus be x km/hr
- The speed of the train is 20% faster than the bus, so the speed of the train is (1 + 20/100) * x = 1.2x km/hr
Calculations:
Let the normal travelling time of the bus be 3t hours and the normal travelling time of the train be 2t hours.
- Distance travelled by the bus in 3t hours = x * 3t
- Distance travelled by the train in 2t hours = 1.2x * 2t
According to the given condition, if the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes.
- New travelling time of the bus = 3t - 24/60 hours
- New travelling time of the train = 2t - 24/60 hours
As the distance covered by both the bus and train remains the same, we can equate the distances:
- x * (3t - 24/60) = 1.2x * (2t - 24/60)
Simplifying the equation:
- 3t - 24/60 = (1.2 * 2t) - 24/60
- 3t - 24/60 = 2.4t - 24/60
- 0.6t = 24/60
- t = (24/60) / 0.6
- t = 24/60 * 10/6
- t = 4/10 * 10/6
- t = 2/3
Therefore, the normal travelling time of the bus, 3t = 3 * (2/3) = 2 hours.
Speed of the bus:
To find the speed of the bus, we can use the formula: Speed = Distance / Time
- Speed of the bus = (Distance travelled by the bus) / (Normal travelling time of the bus)
- Speed of the bus = (x * 3t) / (3t)
- Speed of the bus = x km/hr
Therefore, the speed of the bus is x km/hr.
Conclusion:
The speed of the bus is 75 km/hr.
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Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?Correct answer is '75'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?Correct answer is '75'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?Correct answer is '75'. Can you explain this answer?.
Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?Correct answer is '75'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?Correct answer is '75'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?Correct answer is '75'. Can you explain this answer?.
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Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?Correct answer is '75'. Can you explain this answer?, a detailed solution for Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?Correct answer is '75'. Can you explain this answer? has been provided alongside types of Samrat covers the total journey of 810 km to his village partly by train and then by bus. The train is 20% faster than the bus. If the train were to travel for the number of hours, which normally would be hours travelled by bus, and the bus were to travel the remaining distance, then the time for the journey would reduce by 24 minutes. The normal travelling hours of bus and train are in the ratio 3:2. What is the speed(in km/hr) of the bus?Correct answer is '75'. Can you explain this answer? theory, EduRev gives you an
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