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Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume that whenever a train reaches one city, it leaves for the other city immediately.
- a)1100
- b)1200
- c)1000
- d)1920
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two trains simultaneously leave cities A and B for B and A respectivel...
Because the trains travel at a uniform speed, start together and then meet somewhere, they travel for the same time.
When the time is constant, the distance is proportional to the speed of the trains.
Let the speed of A and B be a and b respectively, and let the distance between the two cities be x km.
When they meet for the first time, train A has covered 500 km and train B has covered (x - 500) km respectively.
When the time is constant, the distance is proportional to the speed of the trains.
Let the speed of A and B be a and b respectively, and let the distance between the two cities be x km.
When they meet for the first time, train A has covered 500 km and train B has covered (x - 500) km respectively.
They meet for the second time at a point that is 400 km away from B.
Hence, train A has first travelled the (x - 500) km to B and then come back another 400 km.
Hence, distance covered by train A between the two meetings = x - 500 + 400 = (x - 100) km. Similarly, distance covered by train B between the two meetings = 500 + x - 400 = (x + 100) km.
Hence, train A has first travelled the (x - 500) km to B and then come back another 400 km.
Hence, distance covered by train A between the two meetings = x - 500 + 400 = (x - 100) km. Similarly, distance covered by train B between the two meetings = 500 + x - 400 = (x + 100) km.
500x + 50000 = x2 - 600x + 50000. x2 - 1100x = 0. Therefore x = 0 or 1100 Since x is the distance between the two cities, x = 1100 cm. Hence, option 1.
Most Upvoted Answer
Two trains simultaneously leave cities A and B for B and A respectivel...
To solve this problem, let's assume the distance between the two cities A and B is x km.
Let the speed of train A be a km/h and the speed of train B be b km/h.
First Meeting:
When the trains meet at a distance of 500 km from city A, train A has traveled x - 500 km and train B has traveled 500 km.
So, the time taken by train A to cover (x - 500) km is (x - 500)/a hours.
Similarly, the time taken by train B to cover 500 km is 500/b hours.
Second Meeting:
When the trains meet at a distance of 400 km from city B, train A has traveled x + 400 km and train B has traveled x - 400 km.
So, the time taken by train A to cover (x + 400) km is (x + 400)/a hours.
Similarly, the time taken by train B to cover (x - 400) km is (x - 400)/b hours.
Since the time taken for both meetings is the same, we can equate the two expressions for time:
(x - 500)/a = (x + 400)/a
Cross-multiplying, we get:
a(x - 500) = b(x + 400)
Expanding, we get:
ax - 500a = bx + 400b
Rearranging, we get:
ax - bx = 400b + 500a
Factoring out x, we get:
x(a - b) = 400b + 500a
Dividing both sides by (a - b), we get:
x = (400b + 500a)/(a - b)
Since the distance between the two cities cannot be negative, we know that a > b.
Given that the answer is 1100 km, we can substitute the values of a and b to check if it satisfies the equation.
Let's assume a = 100 km/h and b = 80 km/h.
Substituting these values, we get:
x = (400 * 80 + 500 * 100)/(100 - 80)
x = (32000 + 50000)/20
x = 82000/20
x = 4100/2
x = 2050
Since the distance between the two cities is 2050 km, which is not the given answer of 1100 km, we need to try another set of values for a and b.
Let's assume a = 120 km/h and b = 100 km/h.
Substituting these values, we get:
x = (400 * 100 + 500 * 120)/(120 - 100)
x = (40000 + 60000)/20
x = 100000/20
x = 5000/2
x = 2500
Since the distance between the two cities is 2500 km, which is also not the given answer of 1100 km, we need to try another set of values for a and b.
Let's assume a = 140 km/h and b = 120 km/h.
Substituting these values, we get:
x = (400 * 120 + 500 * 140)/(140 - 120)
x = (48000 + 70000)/20
x =
Let the speed of train A be a km/h and the speed of train B be b km/h.
First Meeting:
When the trains meet at a distance of 500 km from city A, train A has traveled x - 500 km and train B has traveled 500 km.
So, the time taken by train A to cover (x - 500) km is (x - 500)/a hours.
Similarly, the time taken by train B to cover 500 km is 500/b hours.
Second Meeting:
When the trains meet at a distance of 400 km from city B, train A has traveled x + 400 km and train B has traveled x - 400 km.
So, the time taken by train A to cover (x + 400) km is (x + 400)/a hours.
Similarly, the time taken by train B to cover (x - 400) km is (x - 400)/b hours.
Since the time taken for both meetings is the same, we can equate the two expressions for time:
(x - 500)/a = (x + 400)/a
Cross-multiplying, we get:
a(x - 500) = b(x + 400)
Expanding, we get:
ax - 500a = bx + 400b
Rearranging, we get:
ax - bx = 400b + 500a
Factoring out x, we get:
x(a - b) = 400b + 500a
Dividing both sides by (a - b), we get:
x = (400b + 500a)/(a - b)
Since the distance between the two cities cannot be negative, we know that a > b.
Given that the answer is 1100 km, we can substitute the values of a and b to check if it satisfies the equation.
Let's assume a = 100 km/h and b = 80 km/h.
Substituting these values, we get:
x = (400 * 80 + 500 * 100)/(100 - 80)
x = (32000 + 50000)/20
x = 82000/20
x = 4100/2
x = 2050
Since the distance between the two cities is 2050 km, which is not the given answer of 1100 km, we need to try another set of values for a and b.
Let's assume a = 120 km/h and b = 100 km/h.
Substituting these values, we get:
x = (400 * 100 + 500 * 120)/(120 - 100)
x = (40000 + 60000)/20
x = 100000/20
x = 5000/2
x = 2500
Since the distance between the two cities is 2500 km, which is also not the given answer of 1100 km, we need to try another set of values for a and b.
Let's assume a = 140 km/h and b = 120 km/h.
Substituting these values, we get:
x = (400 * 120 + 500 * 140)/(140 - 120)
x = (48000 + 70000)/20
x =
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Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct answer is option 'A'. Can you explain this answer?
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Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct 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 Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct 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 Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct answer is option 'A'. Can you explain this answer?.
Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct 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 Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct 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 Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct answer is option 'A'. Can you explain this answer?.
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Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Two trains simultaneously leave cities A and B for B and A respectively. Both trains travel at a uniform speed. They meet at a distance 500 km away from city A for the first time. The second time, they meet at a distance 400 km from city B. What is the distance between the two cities (in km)? Assume thatwhenever a train reaches one city, it leaves for the other city immediately.a)1100b)1200c)1000d)1920Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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