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?

Explore Courses CAT Exam CAT Test Series Free Notes EduRev Infinity

Open App

CAT Exam > CAT Questions > A man standing inside a tunnel notices that T...

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?

Join for Free

Join for Free

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.

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 =

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.)

View all questions of this test

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).

Answered by Wizius Careers · View profile

Answer this doubt

Explore Courses for CAT exam

Similar CAT Doubts

A is standing on the foremost point of a train moving at 270 km/hr in a straight line. He starts moving in the direction opposite to that of the train at 3 m/s. At the same time B standing on the rearmost part of the train starts moving in the direction of the train at 4 m/s. A person standing outside notices that when A moves 1800 m, B is 2100 m away from A. Find the length of the train.

View answer

Two persons A and B started running simultaneously from a point P, around a circular track of length 1000 m, in opposite directions, with speeds of 4 m/s and 1 m/s respectively. The moment they crossed each other, two more persons, C and D, started from P towards A and B respectively, C running around the track in the direction opposite to A, with a speed of 1 m/sec and D running around the track, in the direction opposite to B, with a speed of 4 m/sec. Which of the following is a possible time when A, B, C and D will all meet at the same point on the track? (Assume that they continue indefinitely to run around the track in their respective directions).

View answer

2 trains pass through a tunnel at an equal speed of 10 m/s. The first train takes twice as much time as the second train to cross the tunnel completely. The trains can cross each other completely in 2 minutes if they are travelling in the opposite directions on parallel tracks. How much time (in seconds) will a train thrice the length of the shorter train take to cross the tunnel travelling at the same speed as these 2 trains?(Enter 0 if the answer cannot be determine d) Correct answer is '240'. Can you explain this answer?

View answer

Analyse the following passage and provide appropriate answers for the questions that follow:Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected.The principle of science, the definition, almost, is the following: The test of all knowledge is experiment. Experiment is the sole judge of scientific "truth." But what is the source of knowledge? Where do the laws that are to be tested come from? Experiment, itself, helps to produce these laws, in the sense that it gives us hints.But also needed is imagination to create from these hints the great generalizations-to guess at the wonderful, simple, but very strange patterns beneath them all, and then to experiment to check again whether we have made the right guess. This imagining process is so difficult that there is a division of labour in physics: there are theoretical physicists who imagine, deduce, and guess at new laws, but do not experiment; and then there are experimental physicists who experiment, imagine, deduce, and guess.We said that the laws of nature are approximate: that we first find the "wrong" ones, and then we find the "right" ones. Now, how can an experiment be "wrong"? First, in a trivial way: the apparatus can be faulty and you did not notice. But these things are easily fixed and checked back and forth. So without snatching at such minor things, how can the results of an experiment be wrong? Only by being inaccurate. For example, the mass of an object never seems to change; a spinning top has the same weight as a still one. So a "law" was invented: mass is constant, independent of speed. That "law" is now found to be incorrect. Mass is found to increase with velocity, but appreciable increase requires velocities near that of light.A true law is: if an object moves with a speed of less than one hundred miles a second the mass is constant to within one part in a million. In some such approximate form this is a correct law. So in practice one might think that the new law makes no significant difference. Well, yes and no. For ordinary speeds we can certainly forget it and use the simple constant mass law as a good approximation. But for high speeds we are wrong, and the higher the speed, the more wrong we are.Finally, and most interesting, philosophically we are completely wrong with the approximate law. Our entire picture of the world has to be altered even though the mass changes only by a little bit. This is a very peculiar thing about the philosophy, or the ideas, behind the laws.Even a very small effect sometimes requires profound changes to our ideas.Consider the two statements from the passage:Statement I: The mass of an object never seems to change.Statement II: Mass is found to increase with velocity.Q. Which of the following options CANNOT be concluded from the above passage?( d) Statement I reveals that experimental physicists who imagine, deduce, and guess are philosophically wrong.

View answer

Time taken by two trains running in opposite directions to cross a man standing near a pole is 48 seconds and 38 seconds respectively and it took 42 seconds for the trains to cross each other. What is the ratio of the speed of the trains? Correct answer is '2 : 3'. Can you explain this answer?

View answer

Top Courses for CATView all

Quantitative Aptitude (Quant)

CAT Mock Test Series 2025

Crash Course for CAT

Verbal Ability (VA) & Reading Comprehension (RC)

Logical Reasoning (LR) and Data Interpretation (DI)

Top Courses for CAT

Quantitative Aptitude (Quant)

CAT Mock Test Series 2025

Crash Course for CAT

Verbal Ability (VA) & Reading Comprehension (RC)

Logical Reasoning (LR) and Data Interpretation (DI)

View all

Question Description
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?.

Solutions 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? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.

Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of 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 detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an ample number of questions to practice 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? tests, examples and also practice CAT tests.

Explore Courses for CAT exam