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A person travelled a distance of 200 kilometre between two cities by a car covering the first quarter of the journey at a constant speed of 40 km/h and the remaining three quarters at a constant speed of x km/h. If the average speed of the person for the entire journey was 53.33 km/h what is the value of x?
- a)55 km/h
- b)60 km/h
- c)70 km/h
- d)80 km/h
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A person travelled a distance of 200 kilometre between two cities by a...
The total time taken by the motorist would be 200/53.333 = 200 × 3/160 = 3.75 hours = 3 hours 45 minutes.
In the first half of the journey the motorist covers 1/4th the distance @ 40kmph.
This means that he takes 50/40 = 1.25 hours = 1 hour 15 minutes in covering the first 50 kms.
This also means that he covers the remaining distance of 150 km in 2 hours 30 minutes → a speed of 60 kmph.
Hence, option (b) is correct.
In the first half of the journey the motorist covers 1/4th the distance @ 40kmph.
This means that he takes 50/40 = 1.25 hours = 1 hour 15 minutes in covering the first 50 kms.
This also means that he covers the remaining distance of 150 km in 2 hours 30 minutes → a speed of 60 kmph.
Hence, option (b) is correct.
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Community Answer
A person travelled a distance of 200 kilometre between two cities by a...
To find the value of x, we can use the formula for average speed.
Average speed = Total distance / Total time
Let's calculate the total time taken for the journey.
Time taken for the first quarter of the journey = Distance / Speed = 200 km / 40 km/h = 5 hours
Let the time taken for the remaining three quarters of the journey be t hours.
Time taken for the remaining three quarters of the journey = Distance / Speed = 150 km / x km/h = 150/x hours
Total time taken for the journey = Time taken for the first quarter + Time taken for the remaining three quarters
= 5 + 150/x hours
Now, we can calculate the average speed.
Average speed = Total distance / Total time
53.33 km/h = 200 km / (5 + 150/x) hours
Simplifying the equation, we get:
5 + 150/x = 200 / 53.33
5 + 150/x = 3.75
150/x = 3.75 - 5
150/x = -1.25
x/150 = -1/1.25
x = 150 * (-1.25)
x = -187.5
Since speed cannot be negative, we can conclude that there is an error in the question or options provided. None of the given options is correct.
Therefore, the correct answer cannot be determined with the given information.
Average speed = Total distance / Total time
Let's calculate the total time taken for the journey.
Time taken for the first quarter of the journey = Distance / Speed = 200 km / 40 km/h = 5 hours
Let the time taken for the remaining three quarters of the journey be t hours.
Time taken for the remaining three quarters of the journey = Distance / Speed = 150 km / x km/h = 150/x hours
Total time taken for the journey = Time taken for the first quarter + Time taken for the remaining three quarters
= 5 + 150/x hours
Now, we can calculate the average speed.
Average speed = Total distance / Total time
53.33 km/h = 200 km / (5 + 150/x) hours
Simplifying the equation, we get:
5 + 150/x = 200 / 53.33
5 + 150/x = 3.75
150/x = 3.75 - 5
150/x = -1.25
x/150 = -1/1.25
x = 150 * (-1.25)
x = -187.5
Since speed cannot be negative, we can conclude that there is an error in the question or options provided. None of the given options is correct.
Therefore, the correct answer cannot be determined with the given information.
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A person travelled a distance of 200 kilometre between two cities by a car covering the first quarter of the journey at a constant speed of 40 km/h and the remaining three quarters at a constant speed of x km/h. If the average speed of the person for the entire journey was 53.33 km/h what is the value of x?a)55 km/hb)60 km/hc)70 km/hd)80 km/hCorrect answer is option 'B'. Can you explain this answer?
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A person travelled a distance of 200 kilometre between two cities by a car covering the first quarter of the journey at a constant speed of 40 km/h and the remaining three quarters at a constant speed of x km/h. If the average speed of the person for the entire journey was 53.33 km/h what is the value of x?a)55 km/hb)60 km/hc)70 km/hd)80 km/hCorrect 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 A person travelled a distance of 200 kilometre between two cities by a car covering the first quarter of the journey at a constant speed of 40 km/h and the remaining three quarters at a constant speed of x km/h. If the average speed of the person for the entire journey was 53.33 km/h what is the value of x?a)55 km/hb)60 km/hc)70 km/hd)80 km/hCorrect 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 A person travelled a distance of 200 kilometre between two cities by a car covering the first quarter of the journey at a constant speed of 40 km/h and the remaining three quarters at a constant speed of x km/h. If the average speed of the person for the entire journey was 53.33 km/h what is the value of x?a)55 km/hb)60 km/hc)70 km/hd)80 km/hCorrect answer is option 'B'. Can you explain this answer?.
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