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A chartered bus carrying oce employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning by
- a)18% less
- b)30% greater
- c)37.5% greater
- d)50% less
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A chartered bus carrying oce employees travels everyday in two shifts-...
Distance = Speed x Time
In morning slot, Let speed be S and time taken be T, then distance covered = ST
Then, in evening slot, speed will be 1.5S and time taken will be 1.5T, then distance covered = 2.25ST
Hence, the average speed of the bus for the entire journey is greater than its average speed in the morning by 30%
Most Upvoted Answer
A chartered bus carrying oce employees travels everyday in two shifts-...
To solve this problem, let's consider the morning journey first and then analyze the evening journey.
Morning Journey:
Let's assume the morning average speed of the bus is 'x' km/hr.
Let's assume the time taken for the morning journey is 't' hours.
Average speed = Total distance / Total time
=> x = D / t
=> D = x * t ----(1)
Evening Journey:
The evening average speed is 50% greater than the morning average speed, which means it is 1.5 times the morning average speed.
Let the evening average speed be 1.5x km/hr.
The time taken for the evening journey is 50% more than the morning journey, which means it is 1.5 times the morning journey time.
Let the evening journey time be 1.5t hours.
Average speed = Total distance / Total time
=> 1.5x = D / (1.5t)
=> D = 1.5x * 1.5t
=> D = 2.25xt ----(2)
Total Journey:
The total distance covered in the morning and evening journeys is the same, as it is a round trip. Therefore, D in equations (1) and (2) is the same.
Average speed for the entire journey = Total distance / Total time
=> Average speed = 2D / (t + 1.5t)
=> Average speed = 2D / 2.5t
=> Average speed = (2/2.5) * (x * t)
=> Average speed = (4/5) * (x * t)
=> Average speed = 0.8x * t
Comparing this average speed with the morning average speed:
= (0.8x * t) / (x * t) (canceling out t)
= 0.8
Therefore, the average speed for the entire journey is 80% of the morning average speed.
Since 80% is less than 100%, the average speed for the entire journey is 20% less than the morning average speed.
Hence, the correct answer is option 'A' - 18% less.
Morning Journey:
Let's assume the morning average speed of the bus is 'x' km/hr.
Let's assume the time taken for the morning journey is 't' hours.
Average speed = Total distance / Total time
=> x = D / t
=> D = x * t ----(1)
Evening Journey:
The evening average speed is 50% greater than the morning average speed, which means it is 1.5 times the morning average speed.
Let the evening average speed be 1.5x km/hr.
The time taken for the evening journey is 50% more than the morning journey, which means it is 1.5 times the morning journey time.
Let the evening journey time be 1.5t hours.
Average speed = Total distance / Total time
=> 1.5x = D / (1.5t)
=> D = 1.5x * 1.5t
=> D = 2.25xt ----(2)
Total Journey:
The total distance covered in the morning and evening journeys is the same, as it is a round trip. Therefore, D in equations (1) and (2) is the same.
Average speed for the entire journey = Total distance / Total time
=> Average speed = 2D / (t + 1.5t)
=> Average speed = 2D / 2.5t
=> Average speed = (2/2.5) * (x * t)
=> Average speed = (4/5) * (x * t)
=> Average speed = 0.8x * t
Comparing this average speed with the morning average speed:
= (0.8x * t) / (x * t) (canceling out t)
= 0.8
Therefore, the average speed for the entire journey is 80% of the morning average speed.
Since 80% is less than 100%, the average speed for the entire journey is 20% less than the morning average speed.
Hence, the correct answer is option 'A' - 18% less.
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A chartered bus carrying oce employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning bya)18% lessb)30% greaterc)37.5% greaterd)50% lessCorrect answer is option 'B'. Can you explain this answer?
Question Description
A chartered bus carrying oce employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning bya)18% lessb)30% greaterc)37.5% greaterd)50% lessCorrect 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 chartered bus carrying oce employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning bya)18% lessb)30% greaterc)37.5% greaterd)50% lessCorrect 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 chartered bus carrying oce employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning bya)18% lessb)30% greaterc)37.5% greaterd)50% lessCorrect answer is option 'B'. Can you explain this answer?.
A chartered bus carrying oce employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning bya)18% lessb)30% greaterc)37.5% greaterd)50% lessCorrect 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 chartered bus carrying oce employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning bya)18% lessb)30% greaterc)37.5% greaterd)50% lessCorrect 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 chartered bus carrying oce employees travels everyday in two shifts- morning and evening. In the evening, the bus travels at an average speed which is 50% greater than the morning average speed; but takes 50% more time than the amount of time it takes in the morning. The average speed of the chartered bus for the entire journey is greater/less than its average speed in the morning bya)18% lessb)30% greaterc)37.5% greaterd)50% lessCorrect answer is option 'B'. Can you explain this answer?.
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