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A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of 45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?
- a)3 km
- b)4 km
- c)5 km
- d)2 km
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A man standing inside a tunnel notices that Train A is running inside ...
Let the length of Train A be 2L and the length of Train B be L.
According to the given condition,
4 =
Speed of Train A = 45 kmph = 12.5 m/s and speed of Train B = 22.5 m/s
According to the given condition,
4 =
L =
m
Let length of tunnel be t.
So, 4 × 60 =
Putting the value of L in the above equation and solving,
t = 2906.67 m = 2.9 km = 3 km (Approx.)
Most Upvoted Answer
A man standing inside a tunnel notices that Train A is running inside ...
Given:
- Speed of Train A = 45 kmph
- Speed of Train B = 81 kmph
- Train B is half the length of Train A
- Train A passes Train B in 4 seconds
- Train A passes completely through the tunnel in 4 minutes
To find:
- The closest approximation of the length of the tunnel
Let's break down the problem and solve it step by step.
Step 1: Calculate the relative speed of Train A and Train B
The relative speed of two objects moving in opposite directions is the sum of their individual speeds.
Relative speed = Speed of Train A + Speed of Train B
Relative speed = 45 kmph + 81 kmph = 126 kmph
Step 2: Convert the time taken to pass Train B into hours
The time taken to pass Train B is given as 4 seconds. We need to convert it to hours to match the unit of the relative speed.
1 hour = 3600 seconds
Time taken to pass Train B = 4 seconds = 4/3600 hours
Step 3: Calculate the length of Train B
The length of Train B is given as half the length of Train A. Let's assume the length of Train A is 'L'.
Length of Train B = L/2
Step 4: Calculate the length of the tunnel
The total distance covered by Train A to pass Train B and the tunnel is given by the relative speed multiplied by the time taken.
Total distance = Relative speed × Time taken to pass Train B
Total distance = 126 kmph × (4/3600) hours
Now, we know that Train A passes completely through the tunnel in 4 minutes. Since we have the total distance covered by Train A, we can calculate the length of the tunnel using the formula:
Length of tunnel = Total distance - Length of Train B
Step 5: Convert the length of the tunnel into kilometers
To get the length of the tunnel in kilometers, we need to convert it from kilometers per hour to kilometers per minute.
1 hour = 60 minutes
1 kmph = 1/60 km per minute
Finally, we can calculate the length of the tunnel:
Length of tunnel = (Total distance - Length of Train B) × (1/60) km per minute
Simplifying the equation, we get:
Length of tunnel = (Total distance - Length of Train B)/60 km
Substituting the values, we get:
Length of tunnel = [126 kmph × (4/3600) hours - (L/2)]/60 km
Simplifying further, we get:
Length of tunnel = [126 × (4/3600) - (L/2)]/60 km
Length of tunnel = (0.56 - L/2)/60 km
Since we are looking for the closest approximation, we can assume that L is a small fraction compared to 0.56. Hence, we can neglect the L/2 term.
Length of tunnel ≈ 0.56/60 km ≈ 0.00933 km ≈ 3 meters
Therefore, the closest approximation of the length of the tunnel is 3 km (option A).
- Speed of Train A = 45 kmph
- Speed of Train B = 81 kmph
- Train B is half the length of Train A
- Train A passes Train B in 4 seconds
- Train A passes completely through the tunnel in 4 minutes
To find:
- The closest approximation of the length of the tunnel
Let's break down the problem and solve it step by step.
Step 1: Calculate the relative speed of Train A and Train B
The relative speed of two objects moving in opposite directions is the sum of their individual speeds.
Relative speed = Speed of Train A + Speed of Train B
Relative speed = 45 kmph + 81 kmph = 126 kmph
Step 2: Convert the time taken to pass Train B into hours
The time taken to pass Train B is given as 4 seconds. We need to convert it to hours to match the unit of the relative speed.
1 hour = 3600 seconds
Time taken to pass Train B = 4 seconds = 4/3600 hours
Step 3: Calculate the length of Train B
The length of Train B is given as half the length of Train A. Let's assume the length of Train A is 'L'.
Length of Train B = L/2
Step 4: Calculate the length of the tunnel
The total distance covered by Train A to pass Train B and the tunnel is given by the relative speed multiplied by the time taken.
Total distance = Relative speed × Time taken to pass Train B
Total distance = 126 kmph × (4/3600) hours
Now, we know that Train A passes completely through the tunnel in 4 minutes. Since we have the total distance covered by Train A, we can calculate the length of the tunnel using the formula:
Length of tunnel = Total distance - Length of Train B
Step 5: Convert the length of the tunnel into kilometers
To get the length of the tunnel in kilometers, we need to convert it from kilometers per hour to kilometers per minute.
1 hour = 60 minutes
1 kmph = 1/60 km per minute
Finally, we can calculate the length of the tunnel:
Length of tunnel = (Total distance - Length of Train B) × (1/60) km per minute
Simplifying the equation, we get:
Length of tunnel = (Total distance - Length of Train B)/60 km
Substituting the values, we get:
Length of tunnel = [126 kmph × (4/3600) hours - (L/2)]/60 km
Simplifying further, we get:
Length of tunnel = [126 × (4/3600) - (L/2)]/60 km
Length of tunnel = (0.56 - L/2)/60 km
Since we are looking for the closest approximation, we can assume that L is a small fraction compared to 0.56. Hence, we can neglect the L/2 term.
Length of tunnel ≈ 0.56/60 km ≈ 0.00933 km ≈ 3 meters
Therefore, the closest approximation of the length of the tunnel is 3 km (option A).
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A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of 45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?a)3 kmb)4 kmc)5 kmd)2 kmCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of 45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?a)3 kmb)4 kmc)5 kmd)2 kmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of 45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?a)3 kmb)4 kmc)5 kmd)2 kmCorrect answer is option 'A'. Can you explain this answer?.
A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of 45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?a)3 kmb)4 kmc)5 kmd)2 kmCorrect answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of 45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?a)3 kmb)4 kmc)5 kmd)2 kmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of 45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?a)3 kmb)4 kmc)5 kmd)2 kmCorrect answer is option 'A'. Can you explain this answer?.
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