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A pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithan which are 40 km apart and meet 2 hours after the start. Then they resumed their trips and the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. Which of these could be the speed of the pedestrian?
- a)4 km/h
- b)5 km/h
- c)3 km/h
- d)6 km/h
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A pedestrian and a cyclist start simultaneously towards each other fro...
The relative speed is 20 kmph. Also, the pedestrian should take 7:30 hours more than the cyclist.
Using option (a) the speeds of the two people are 4km/hr and 16 km/hr respectively.
At this speed, the respective times would be 10 hrs and 2:30 hours, giving the required answer.
Using option (a) the speeds of the two people are 4km/hr and 16 km/hr respectively.
At this speed, the respective times would be 10 hrs and 2:30 hours, giving the required answer.
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A pedestrian and a cyclist start simultaneously towards each other fro...
To solve this problem, let's break it down into two parts: the initial meeting and the subsequent travel time.
1. Initial Meeting:
- Let's assume the speed of the pedestrian is P km/h and the speed of the cyclist is C km/h.
- The time taken by the pedestrian to meet the cyclist is 2 hours.
- Thus, in these 2 hours, the pedestrian travels a distance of 2P km and the cyclist travels a distance of 2C km.
- The total distance between Aurangabad and Paithan is 40 km, so we can write the equation: 2P + 2C = 40.
2. Subsequent Travel Time:
- The cyclist arrives at Aurangabad 7 hours 30 minutes (or 7.5 hours) earlier than the pedestrian arrives at Paithan.
- Let's assume the time taken by the pedestrian to reach Paithan is T hours.
- The time taken by the cyclist to reach Aurangabad is T + 7.5 hours.
- We know that distance = speed × time, so we can write the equations: P × T = 40 and C × (T + 7.5) = 40.
Now, let's solve these equations to find the value of P.
From the equation P × T = 40, we can express T in terms of P: T = 40/P.
Substituting this value of T in the equation C × (T + 7.5) = 40, we get C × (40/P + 7.5) = 40.
Simplifying this equation, we have 40C + 7.5C = 40P.
Now, let's substitute the value of C from the first equation (2P + 2C = 40): 40(2P + 2C) + 7.5C = 40P.
Expanding this equation, we get 80P + 80C + 7.5C = 40P.
Simplifying further, we have 40P + 87.5C = 0.
Since P and C are speeds, they cannot be negative. Therefore, the only possible solution is when C = 0.
Substituting C = 0 in the first equation (2P + 2C = 40), we get 2P = 40, or P = 20/2 = 10.
However, the options provided for the speed of the pedestrian are 4 km/h, 5 km/h, 3 km/h, and 6 km/h. None of these options match the calculated speed of 10 km/h.
Hence, there seems to be an error in the given options, and we cannot determine the speed of the pedestrian with the given information.
1. Initial Meeting:
- Let's assume the speed of the pedestrian is P km/h and the speed of the cyclist is C km/h.
- The time taken by the pedestrian to meet the cyclist is 2 hours.
- Thus, in these 2 hours, the pedestrian travels a distance of 2P km and the cyclist travels a distance of 2C km.
- The total distance between Aurangabad and Paithan is 40 km, so we can write the equation: 2P + 2C = 40.
2. Subsequent Travel Time:
- The cyclist arrives at Aurangabad 7 hours 30 minutes (or 7.5 hours) earlier than the pedestrian arrives at Paithan.
- Let's assume the time taken by the pedestrian to reach Paithan is T hours.
- The time taken by the cyclist to reach Aurangabad is T + 7.5 hours.
- We know that distance = speed × time, so we can write the equations: P × T = 40 and C × (T + 7.5) = 40.
Now, let's solve these equations to find the value of P.
From the equation P × T = 40, we can express T in terms of P: T = 40/P.
Substituting this value of T in the equation C × (T + 7.5) = 40, we get C × (40/P + 7.5) = 40.
Simplifying this equation, we have 40C + 7.5C = 40P.
Now, let's substitute the value of C from the first equation (2P + 2C = 40): 40(2P + 2C) + 7.5C = 40P.
Expanding this equation, we get 80P + 80C + 7.5C = 40P.
Simplifying further, we have 40P + 87.5C = 0.
Since P and C are speeds, they cannot be negative. Therefore, the only possible solution is when C = 0.
Substituting C = 0 in the first equation (2P + 2C = 40), we get 2P = 40, or P = 20/2 = 10.
However, the options provided for the speed of the pedestrian are 4 km/h, 5 km/h, 3 km/h, and 6 km/h. None of these options match the calculated speed of 10 km/h.
Hence, there seems to be an error in the given options, and we cannot determine the speed of the pedestrian with the given information.
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A pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithan which are 40 km apart and meet 2 hours after the start. Then they resumed their trips and the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. Which of these could be the speed of the pedestrian?a)4 km/hb)5 km/hc)3 km/hd)6 km/hCorrect answer is option 'A'. Can you explain this answer?
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A pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithan which are 40 km apart and meet 2 hours after the start. Then they resumed their trips and the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. Which of these could be the speed of the pedestrian?a)4 km/hb)5 km/hc)3 km/hd)6 km/hCorrect answer is option 'A'. 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 pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithan which are 40 km apart and meet 2 hours after the start. Then they resumed their trips and the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. Which of these could be the speed of the pedestrian?a)4 km/hb)5 km/hc)3 km/hd)6 km/hCorrect answer is option 'A'. 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 pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithan which are 40 km apart and meet 2 hours after the start. Then they resumed their trips and the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. Which of these could be the speed of the pedestrian?a)4 km/hb)5 km/hc)3 km/hd)6 km/hCorrect answer is option 'A'. Can you explain this answer?.
A pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithan which are 40 km apart and meet 2 hours after the start. Then they resumed their trips and the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. Which of these could be the speed of the pedestrian?a)4 km/hb)5 km/hc)3 km/hd)6 km/hCorrect answer is option 'A'. 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 pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithan which are 40 km apart and meet 2 hours after the start. Then they resumed their trips and the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. Which of these could be the speed of the pedestrian?a)4 km/hb)5 km/hc)3 km/hd)6 km/hCorrect answer is option 'A'. 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 pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithan which are 40 km apart and meet 2 hours after the start. Then they resumed their trips and the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. Which of these could be the speed of the pedestrian?a)4 km/hb)5 km/hc)3 km/hd)6 km/hCorrect answer is option 'A'. Can you explain this answer?.
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