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Trains A and B start from Chennai and Hyderabad towards Hyderabad and Chennai respectively. Train A has 3 stops between Chennai and Hyderabad. The distance between any 2 stops is exactly 25% of the overall distance between Chennai and Hyderabad. Train B has 4 stops, and distance between any 2 stops is exactly equal to 20% of the overall distance. Train A starts at 11 AM, while Train B starts at 1 PM. Distance between Chennai and Hyderabad is 800 kms.
Due to a failure in the engine, Train A has to wait at its 1st stop for 1 hour, while it waits for 15 minutes at all other stops. Train B waits 5 minutes at all its stops.
Q. If Speed of Train A is 100 kmph, and speed of Train B is 60% more than that of Train A, at approximately what distance from Chennai will the trains cross each other?
  • a)
    350 Kms
  • b)
    360 Kms
  • c)
    370 Kms
  • d)
    380 Kms
  • e)
    390 Kms
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Trains A and B start from Chennai and Hyderabad towards Hyderabad and...
Overview
To find the distance at which Train A and Train B cross each other, we need to calculate the time taken by both trains to reach the crossing point.
Distance and Stops
- Distance between Chennai and Hyderabad: 800 km
- Train A stops: 3 stops (25% distance between stops)
- Train B stops: 4 stops (20% distance between stops)
Speed of Trains
- Speed of Train A: 100 km/h
- Speed of Train B: 60% more than Train A, which calculates to:
- Speed of Train B = 100 km/h + (0.6 * 100 km/h) = 160 km/h
Time Calculation for Train A
- Total stops delay for Train A:
- 1st stop: 1 hour
- 2nd & 3rd stops: 15 minutes each = 0.25 hours
- Total delay = 1 + 0.25 + 0.25 = 1.5 hours
- Total travel time (without stops) for Train A to cover 800 km:
- Time = Distance/Speed = 800 km / 100 km/h = 8 hours
- Effective travel time for Train A = 8 + 1.5 = 9.5 hours
Time Calculation for Train B
- Total stops delay for Train B:
- Each stop: 5 minutes = 1/12 hours
- Total delay = 4 stops * (1/12) = 1/3 hours
- Total travel time (without stops) for Train B:
- Time = Distance/Speed = 800 km / 160 km/h = 5 hours
- Effective travel time for Train B = 5 + 1/3 = 5.33 hours
Crossing Point Calculation
- Train A starts at 11 AM. By the time Train B starts at 1 PM, Train A has been traveling for 2 hours (covering 200 km).
- Remaining distance for Train A = 600 km. Time to cover this = 6 hours (600 km / 100 km/h).
- Train B travels for x hours after starting at 1 PM.
Now, to find when they meet:
- Distance covered by Train B after x hours: 160x km.
- They meet when:
- 200 km + 100 * (x + 2) = 160x
- Simplifying gives: 200 + 100x + 200 = 160x
- Rearranging: 400 = 60x, thus x = 400/60 ≈ 6.67 hours.
Final Distance Calculation
- Distance from Chennai when they meet:
- Distance = 200 km (Train A's first part) + 100 km/h * 6.67h = 200 + 667 ≈ 380 km.
Thus, the trains will cross each other at approximately 380 km from Chennai, confirming option D.
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Community Answer
Trains A and B start from Chennai and Hyderabad towards Hyderabad and...
Train A stops after every 200 Km, and train B stops after every 160 km.
Speed of train A = 100 kmph
Speed of train B = 100 x 1.6 = 160 kmph
Time B leaves its first stop = 1PM + 160/160 hrs + 5 minutes break = 2:05 PM
So, at 2:05PM, Train B will be at 160 Km from Hyderabad
Similarly, at 3:10 PM, it will be leaving its 2nd stop, 320 km from Hyderabad.
At 3:10 PM, lets check where Train A will be:
Time to reach stop 1 = 11 AM + 200/100 hours = 1 PM
Time to leave stop 1 = 1 PM + 1 hr = 2 PM
At, 3:10 PM, it will be at 200 kms + (100 kmph x (70 mins/60 mins)) = 316.67 Km from Chennai
Next stop for Train A = 4PM, for B = 4:10 PM.
Distance between trains = 800 - (320 + 316.67) = 163.32 Km
Relative speed = 100 + 160 = 260 kmph
Time to cover 163.62 km = 37.69 mins
Train A would have covered 316.67 kms + 100 x 37.69/60 = 379 Kms ~ 380 kms.
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Trains A and B start from Chennai and Hyderabad towards Hyderabad and Chennai respectively. Train A has 3 stops between Chennai and Hyderabad. The distance between any 2 stops is exactly 25% of the overall distance between Chennai and Hyderabad. Train B has 4 stops, and distance between any 2 stops is exactly equal to 20% of the overall distance. Train A starts at 11 AM, while Train B starts at 1 PM. Distance between Chennai and Hyderabad is 800 kms.Due to a failure in the engine, Train A has to wait at its 1st stop for 1 hour, while it waits for 15 minutes at all other stops. Train B waits 5 minutes at all its stops.Q. If Speed of Train A is 100 kmph, and speed of Train B is 60% more than that of Train A, at approximately what distance from Chennai will the trains cross each other?a)350 Kmsb)360 Kmsc)370 Kmsd)380 Kmse)390 KmsCorrect answer is option 'D'. Can you explain this answer?
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Trains A and B start from Chennai and Hyderabad towards Hyderabad and Chennai respectively. Train A has 3 stops between Chennai and Hyderabad. The distance between any 2 stops is exactly 25% of the overall distance between Chennai and Hyderabad. Train B has 4 stops, and distance between any 2 stops is exactly equal to 20% of the overall distance. Train A starts at 11 AM, while Train B starts at 1 PM. Distance between Chennai and Hyderabad is 800 kms.Due to a failure in the engine, Train A has to wait at its 1st stop for 1 hour, while it waits for 15 minutes at all other stops. Train B waits 5 minutes at all its stops.Q. If Speed of Train A is 100 kmph, and speed of Train B is 60% more than that of Train A, at approximately what distance from Chennai will the trains cross each other?a)350 Kmsb)360 Kmsc)370 Kmsd)380 Kmse)390 KmsCorrect answer is option 'D'. 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 Trains A and B start from Chennai and Hyderabad towards Hyderabad and Chennai respectively. Train A has 3 stops between Chennai and Hyderabad. The distance between any 2 stops is exactly 25% of the overall distance between Chennai and Hyderabad. Train B has 4 stops, and distance between any 2 stops is exactly equal to 20% of the overall distance. Train A starts at 11 AM, while Train B starts at 1 PM. Distance between Chennai and Hyderabad is 800 kms.Due to a failure in the engine, Train A has to wait at its 1st stop for 1 hour, while it waits for 15 minutes at all other stops. Train B waits 5 minutes at all its stops.Q. If Speed of Train A is 100 kmph, and speed of Train B is 60% more than that of Train A, at approximately what distance from Chennai will the trains cross each other?a)350 Kmsb)360 Kmsc)370 Kmsd)380 Kmse)390 KmsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Trains A and B start from Chennai and Hyderabad towards Hyderabad and Chennai respectively. Train A has 3 stops between Chennai and Hyderabad. The distance between any 2 stops is exactly 25% of the overall distance between Chennai and Hyderabad. Train B has 4 stops, and distance between any 2 stops is exactly equal to 20% of the overall distance. Train A starts at 11 AM, while Train B starts at 1 PM. Distance between Chennai and Hyderabad is 800 kms.Due to a failure in the engine, Train A has to wait at its 1st stop for 1 hour, while it waits for 15 minutes at all other stops. Train B waits 5 minutes at all its stops.Q. If Speed of Train A is 100 kmph, and speed of Train B is 60% more than that of Train A, at approximately what distance from Chennai will the trains cross each other?a)350 Kmsb)360 Kmsc)370 Kmsd)380 Kmse)390 KmsCorrect answer is option 'D'. Can you explain this answer?.
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