All Courses
Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity Get the App Login Join for Free
Sign in Open App
CAT Exam  >  CAT Questions  >  Samrat covers the total journey of 810 km to ... Start Learning for Free
SaveJoin the Discussion on the App
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?
    FREE This question is part of
    Download PDF Attempt Test
    		Download PDF Attempt this Test
    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,

    5.6xb - 810 = 0.4b
    5.6(150) -810 = 0.4b 
    b = 75
    The speed of the bus = 75 km/hr 
    Answer: 75
    View all questions of this test
    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.
    Free Test
    FREE
    Start Free Test
    		Start Free Test
    Community Answer
    Samrat covers the total journey of 810 km to his village partly by tra...
    75
    Attention CAT Students!
    To make sure you are not studying endlessly, EduRev has designed CAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CAT.
    < Previous Question Next Question >
    Explore Courses for CAT exam

    Similar CAT Doubts

    Directions : Ten pilgrims A, B, C, D, E, F, G, H, I and J visited Haridwar on either 10th or 24th of January, February, March, April and May not necessarily in the same order. They took a train journey to Haridwar from their hometown. Each took a different time in hours (integral valu e) to reach the destination. Pilgrims taking a consecutive number of hours did not travel on consecutive turns. A person taking an odd number of hours travelled in a month with an odd number of days and a person taking an even number of hours travelled in a month with an even number of days. Consider the year to be 2017. A took 33 hours to reach his destination A and H had their journeys at a gap of 2 persons Number of persons who travelled after J was one more than the number of persons who travelled before H. J travelled after H F and E travelled at a gap of 1 person and F took 7 hours more than that taken by E to reach the destination A and F took consecutive number of hours. J and C travelled in consecutive months but not on consecutive turns C took 8 hours less than that taken by D who travelled on March 24 Journey taken on February 10 was of 32 hours B took 36 hours to complete his journey B and I travelled at a gap of 2 persons G took 19 hours to reach his destination I travelled at a gap of 1 person from the one who took a journey of 29 hours H took 2 hours less than that taken by D who took less than 30 hours to complete his journey The person travelling on 24th February took 24 hours to complete his journey C and J took consecutive number of hours.How many hours did J take to complete his journey?

    Directions : Ten pilgrims A, B, C, D, E, F, G, H, I and J visited Haridwar on either 10th or 24th of months of January, February, March, April and May not necessarily in the same order. They took a train journey to Haridwar from their hometown. Each took a different time in hours (integral valu e) to reach the destination. Pilgrims taking a consecutive number of hours did not travel on consecutive turns. A person taking an odd number of hours travelled in a month with an odd number of days and a person taking an even number of hours travelled in a month with an even number of days. Consider the year to be 2017. A took 33 hours to reach his destination A and H had their journeys at a gap of 2 persons Number of persons who travelled after J was one more than the number of persons who travelled before H. J travelled after H F and E travelled at a gap of 1 person and F took 7 hours more than that taken by E to reach the destination A and F took consecutive number of hours. J and C travelled in consecutive months but not on consecutive turns C took 8 hours less than that taken by D who travelled on March 24 Journey taken on February 10 was of 32 hours B took 36 hours to complete his journey B and I travelled at a gap of 2 persons G took 19 hours to reach his destination I travelled at a gap of 1 person from the one who took a journey of 29 hours H took 2 hours less than that taken by D who took less than 30 hours to complete his journey The person travelling on 24th February took 24 hours to complete his journey C and J took consecutive number of hours.What was the difference between the travel time of H and E?

    Directions: Ten pilgrims A, B, C, D, E, F, G, H, I and J visited Haridwar on either 10th or 24th of months of January, February, March, April and May not necessarily in the same order. They took a train journey to Haridwar from their hometown. Each took a different time in hours (integral valu e) to reach the destination. Pilgrims taking consecutive number of hours did not travel on consecutive turns. A person taking odd number of hours travelled in a month with odd number of days and a person taking even number of hours travelled in a month with even number of days. Consider the year to be 2017. A took 33 hours to reach his destination A and H had their journeys at a gap of 2 persons Number of persons who travelled after J was one more than the number of persons who travelled before H. J travelled after H F and E travelled at a gap of 1 person and F took 7 hours more than that taken by E to reach the destination A and F took consecutive number of hours. J and C travelled in consecutive months but not on consecutive turns C took 8 hours less than that taken by D who travelled on March 24 Journey taken on February 10 was of 32 hours B took 36 hours to complete his journey B and I travelled at a gap of 2 persons G took 19 hours to reach his destination I travelled at a gap of 1 person from the one who took a journey of 29 hours H took 2 hours less than that taken by D who took less than 30 hours to complete his journey The person travelling on 24th February took 24 hours to complete his journey C and J took consecutive number of hours. Q. How many hours did J take to complete his journey?

    Directions: Ten pilgrims A, B, C, D, E, F, G, H, I and J visited Haridwar on either 10th or 24th of months of January, February, March, April and May not necessarily in the same order. They took a train journey to Haridwar from their hometown. Each took a different time in hours (integral valu e) to reach the destination. Pilgrims taking consecutive number of hours did not travel on consecutive turns. A person taking odd number of hours travelled in a month with odd number of days and a person taking even number of hours travelled in a month with even number of days. Consider the year to be 2017. A took 33 hours to reach his destination A and H had their journeys at a gap of 2 persons Number of persons who travelled after J was one more than the number of persons who travelled before H. J travelled after H F and E travelled at a gap of 1 person and F took 7 hours more than that taken by E to reach the destination A and F took consecutive number of hours. J and C travelled in consecutive months but not on consecutive turns C took 8 hours less than that taken by D who travelled on March 24 Journey taken on February 10 was of 32 hours B took 36 hours to complete his journey B and I travelled at a gap of 2 persons G took 19 hours to reach his destination I travelled at a gap of 1 person from the one who took a journey of 29 hours H took 2 hours less than that taken by D who took less than 30 hours to complete his journey The person travelling on 24th February took 24 hours to complete his journey C and J took consecutive number of hours. Q. What was the difference between the travel time of H and E?

    Directions: Ten pilgrims A, B, C, D, E, F, G, H, I and J visited Haridwar on either 10th or 24th of January, February, March, April and May not necessarily in the same order. They took a train journey to Haridwar from their hometown. Each took a different time in hours (integral valu e) to reach the destination. Pilgrims taking a consecutive number of hours did not travel on consecutive turns. A person taking an odd number of hours travelled in a month with an odd number of days and a person taking an even number of hours travelled in a month with an even number of days. Consider the year to be 2017. A took 33 hours to reach his destination A and H had their journeys at a gap of 2 persons Number of persons who travelled after J was one more than the number of persons who travelled before H. J travelled after H F and E travelled at a gap of 1 person and F took 7 hours more than that taken by E to reach the destination A and F took consecutive number of hours. J and C travelled in consecutive months but not on consecutive turns C took 8 hours less than that taken by D who travelled on March 24 Journey taken on February 10 was of 32 hours B took 36 hours to complete his journey B and I travelled at a gap of 2 persons G took 19 hours to reach his destination I travelled at a gap of 1 person from the one who took a journey of 29 hours H took 2 hours less than that taken by D who took less than 30 hours to complete his journey The person travelling on 24th February took 24 hours to complete his journey C and J took consecutive number of hours. Who among the following travelled on February 10th?

    Top Courses for CATView all

    Top Courses for CAT

    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?
    Question Description
    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 2024 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 2024 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?.
    Solutions 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? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
    Here you can find the meaning 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? defined & explained in the simplest way possible. Besides giving the explanation 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?, 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 ample number of questions to practice 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? tests, examples and also practice CAT tests.
    Explore Courses for CAT exam

    Top Courses for CAT

    Explore Courses

    Suggested Free Tests

    Signup for Free!
    Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
    10M+ students study on EduRev
    Get App
    © EduRev
    Education Revolution
    Follow Us
    Signup to see your scores go up within 7 days!
    Access 1000+ FREE Docs, Videos and Tests
    Takes less than 10 seconds to signup