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Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total journey by Car and rest of the journey by Train. If the speeds of the Train, Car and Bus are 60 km/hr, 80 km/hr and 50 km/hr respectively then what was the average speed of Rahim during the entire journey?
- a)62.5 km/hr
- b)58.5 km/hr
- c)55.5 km/hr
- d)65 km/hr
- e)None of These
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total jo...
Let the total distance be 6d km.
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Hence the distance covered by bus = 2d km
Since speed of the bus = 50 km/hr
Hence time taken by bus, T1 = 2d/50 = d/25 hours
Similarly time taken by car, T2 = d/80 hours
Similarly time taken by train, T3 = 3d/60 = d/20 hours
Average speed = Total distance/Total time 6dd/25 + d/80 + d/20 = 58.5 km/hr
Most Upvoted Answer
Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total jo...
Understanding the Journey Breakdown
Rahim's journey is divided as follows:
- By Bus: 1/3 of the total journey
- By Car: 1/6 of the total journey
- By Train: Remaining distance
Calculating the Distance by Each Mode
Assuming the total distance (D) is 1 unit (for simplicity):
- Distance by Bus = (1/3)D
- Distance by Car = (1/6)D
- Remaining distance by Train = D - (1/3)D - (1/6)D
To simplify the remaining distance:
- Common denominator = 6
- Distance by Bus = 2/6 D
- Distance by Car = 1/6 D
- Remaining distance = D - (2/6 + 1/6)D = (3/6)D = 1/2 D
Thus, the distances covered are:
- Bus: 1/3 D
- Car: 1/6 D
- Train: 1/2 D
Calculating Time Taken for Each Segment
Using speeds of each mode:
- Bus Speed: 50 km/hr
- Car Speed: 80 km/hr
- Train Speed: 60 km/hr
Time = Distance / Speed
- Time by Bus: (1/3)D / 50 = D / 150 hours
- Time by Car: (1/6)D / 80 = D / 480 hours
- Time by Train: (1/2)D / 60 = D / 120 hours
Total Time Taken
Total time = Time by Bus + Time by Car + Time by Train
= D/150 + D/480 + D/120
To calculate the total time, find a common denominator (which is 480):
- Total time = (3.2D + D + 4D) / 480 = (8.2D) / 480 = 0.0170833D hours
Average Speed Calculation
Average speed = Total distance / Total time
Average speed = D / (0.0170833D) = 58.5 km/hr
Thus, the average speed of Rahim during the entire journey is 58.5 km/hr (Option B).
Rahim's journey is divided as follows:
- By Bus: 1/3 of the total journey
- By Car: 1/6 of the total journey
- By Train: Remaining distance
Calculating the Distance by Each Mode
Assuming the total distance (D) is 1 unit (for simplicity):
- Distance by Bus = (1/3)D
- Distance by Car = (1/6)D
- Remaining distance by Train = D - (1/3)D - (1/6)D
To simplify the remaining distance:
- Common denominator = 6
- Distance by Bus = 2/6 D
- Distance by Car = 1/6 D
- Remaining distance = D - (2/6 + 1/6)D = (3/6)D = 1/2 D
Thus, the distances covered are:
- Bus: 1/3 D
- Car: 1/6 D
- Train: 1/2 D
Calculating Time Taken for Each Segment
Using speeds of each mode:
- Bus Speed: 50 km/hr
- Car Speed: 80 km/hr
- Train Speed: 60 km/hr
Time = Distance / Speed
- Time by Bus: (1/3)D / 50 = D / 150 hours
- Time by Car: (1/6)D / 80 = D / 480 hours
- Time by Train: (1/2)D / 60 = D / 120 hours
Total Time Taken
Total time = Time by Bus + Time by Car + Time by Train
= D/150 + D/480 + D/120
To calculate the total time, find a common denominator (which is 480):
- Total time = (3.2D + D + 4D) / 480 = (8.2D) / 480 = 0.0170833D hours
Average Speed Calculation
Average speed = Total distance / Total time
Average speed = D / (0.0170833D) = 58.5 km/hr
Thus, the average speed of Rahim during the entire journey is 58.5 km/hr (Option B).
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Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total journey by Car and rest of the journey by Train. If the speeds of the Train, Car and Bus are 60 km/hr, 80 km/hr and 50 km/hr respectively then what was the average speed of Rahim during the entire journey?a) 62.5 km/hrb) 58.5 km/hrc) 55.5 km/hrd) 65 km/hre) None of TheseCorrect answer is option 'B'. Can you explain this answer?
Question Description
Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total journey by Car and rest of the journey by Train. If the speeds of the Train, Car and Bus are 60 km/hr, 80 km/hr and 50 km/hr respectively then what was the average speed of Rahim during the entire journey?a) 62.5 km/hrb) 58.5 km/hrc) 55.5 km/hrd) 65 km/hre) None of TheseCorrect answer is option 'B'. 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 Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total journey by Car and rest of the journey by Train. If the speeds of the Train, Car and Bus are 60 km/hr, 80 km/hr and 50 km/hr respectively then what was the average speed of Rahim during the entire journey?a) 62.5 km/hrb) 58.5 km/hrc) 55.5 km/hrd) 65 km/hre) None of TheseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total journey by Car and rest of the journey by Train. If the speeds of the Train, Car and Bus are 60 km/hr, 80 km/hr and 50 km/hr respectively then what was the average speed of Rahim during the entire journey?a) 62.5 km/hrb) 58.5 km/hrc) 55.5 km/hrd) 65 km/hre) None of TheseCorrect answer is option 'B'. Can you explain this answer?.
Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total journey by Car and rest of the journey by Train. If the speeds of the Train, Car and Bus are 60 km/hr, 80 km/hr and 50 km/hr respectively then what was the average speed of Rahim during the entire journey?a) 62.5 km/hrb) 58.5 km/hrc) 55.5 km/hrd) 65 km/hre) None of TheseCorrect answer is option 'B'. 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 Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total journey by Car and rest of the journey by Train. If the speeds of the Train, Car and Bus are 60 km/hr, 80 km/hr and 50 km/hr respectively then what was the average speed of Rahim during the entire journey?a) 62.5 km/hrb) 58.5 km/hrc) 55.5 km/hrd) 65 km/hre) None of TheseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rahim covers 1/3rd of his total journey by Bus, 1/6th of his total journey by Car and rest of the journey by Train. If the speeds of the Train, Car and Bus are 60 km/hr, 80 km/hr and 50 km/hr respectively then what was the average speed of Rahim during the entire journey?a) 62.5 km/hrb) 58.5 km/hrc) 55.5 km/hrd) 65 km/hre) None of TheseCorrect answer is option 'B'. Can you explain this answer?.
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