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A pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithanwhich are 40 km apart and meet 2 hours after the start. Then they resumed their trips and thecyclist 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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Given information:
- Distance between Aurangabad and Paithan = 40 km
- They meet 2 hours after the start
- Cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan
To find:
Which of these could be the speed of the pedestrian?
Let's assume that the speed of the pedestrian is x km/hr and the speed of the cyclist is y km/hr.
Calculation:
- In the first 2 hours, the pedestrian and the cyclist together cover a distance of 2(x+y) km, as they are moving towards each other.
- Therefore, the remaining distance between Aurangabad and Paithan is 40 - 2(x+y) km.
- Let's calculate the time taken by the pedestrian to cover this distance. We know that the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. So, the time taken by the cyclist to cover the distance between Aurangabad and Paithan is (7.5 + t) hours, where t is the time taken by the pedestrian.
- We can write the following equation to find the value of t:
(40 - 2(x+y))/x = t + 7.5
(40 - 2(x+y))/x - t = 7.5
- Now, let's use the equation of speed to find the value of y:
y = (40 - 2(x+y))/(2+t)
- Simplifying the above equation, we get:
y = (40 - 2x - 2y)/(t+2)
y(t+2) = 40 - 2x - 2y
yt + 2y = 40 - 2x
y(t+2) + 2x = 40
- We know that the speed of the cyclist is greater than the speed of the pedestrian, so y > x.
- Let's substitute the value of t in the above equation using the equation we derived earlier:
(40 - 2(x+y))/x - 7.5 = y
40/x - 2 - 2y/x - 7.5 = y
40/x - 2y/x - 9.5 = y
40 - 2y - 9.5x = xy
- We can now substitute the value of y(t+2) + 2x = 40 in the above equation:
(40-2x)/3 - 2y/3 - 9.5x = xy
40 - 6x - 6y - 28.5x = 3xy
40 - 34.5x = 9xy
- Substituting y = (40-2x)/(t+2) in the above equation:
40 - 34.5x = 9x(40-2x)/(t+2)
40(t+2) - 34.5xt - 9x(40-2x) = 0
40t - 5.5xt - x(40-2x) = 0
- We can now substitute the value of t = (40 - 2(x+y))/x - 7.
- Distance between Aurangabad and Paithan = 40 km
- They meet 2 hours after the start
- Cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan
To find:
Which of these could be the speed of the pedestrian?
Let's assume that the speed of the pedestrian is x km/hr and the speed of the cyclist is y km/hr.
Calculation:
- In the first 2 hours, the pedestrian and the cyclist together cover a distance of 2(x+y) km, as they are moving towards each other.
- Therefore, the remaining distance between Aurangabad and Paithan is 40 - 2(x+y) km.
- Let's calculate the time taken by the pedestrian to cover this distance. We know that the cyclist arrives at Aurangabad 7 hours 30 minutes earlier than the pedestrian arrives at Paithan. So, the time taken by the cyclist to cover the distance between Aurangabad and Paithan is (7.5 + t) hours, where t is the time taken by the pedestrian.
- We can write the following equation to find the value of t:
(40 - 2(x+y))/x = t + 7.5
(40 - 2(x+y))/x - t = 7.5
- Now, let's use the equation of speed to find the value of y:
y = (40 - 2(x+y))/(2+t)
- Simplifying the above equation, we get:
y = (40 - 2x - 2y)/(t+2)
y(t+2) = 40 - 2x - 2y
yt + 2y = 40 - 2x
y(t+2) + 2x = 40
- We know that the speed of the cyclist is greater than the speed of the pedestrian, so y > x.
- Let's substitute the value of t in the above equation using the equation we derived earlier:
(40 - 2(x+y))/x - 7.5 = y
40/x - 2 - 2y/x - 7.5 = y
40/x - 2y/x - 9.5 = y
40 - 2y - 9.5x = xy
- We can now substitute the value of y(t+2) + 2x = 40 in the above equation:
(40-2x)/3 - 2y/3 - 9.5x = xy
40 - 6x - 6y - 28.5x = 3xy
40 - 34.5x = 9xy
- Substituting y = (40-2x)/(t+2) in the above equation:
40 - 34.5x = 9x(40-2x)/(t+2)
40(t+2) - 34.5xt - 9x(40-2x) = 0
40t - 5.5xt - x(40-2x) = 0
- We can now substitute the value of t = (40 - 2(x+y))/x - 7.
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A pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithanwhich are 40 km apart and meet 2 hours after the start. Then they resumed their trips and thecyclist 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 Paithanwhich are 40 km apart and meet 2 hours after the start. Then they resumed their trips and thecyclist 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 Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithanwhich are 40 km apart and meet 2 hours after the start. Then they resumed their trips and thecyclist 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 Quant 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 Paithanwhich are 40 km apart and meet 2 hours after the start. Then they resumed their trips and thecyclist 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 Paithanwhich are 40 km apart and meet 2 hours after the start. Then they resumed their trips and thecyclist 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 Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A pedestrian and a cyclist start simultaneously towards each other from Aurangabad and Paithanwhich are 40 km apart and meet 2 hours after the start. Then they resumed their trips and thecyclist 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 Quant 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 Paithanwhich are 40 km apart and meet 2 hours after the start. Then they resumed their trips and thecyclist 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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