__Question:__A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

**Options:**

A. | 130 | |

B. | 360 | |

C. | 500 | |

D. | 540 |

**Answer: Option C**

Speed =\(\left(78\times\frac{5}{18}\right)m/sec = \left(\frac{65}{3}\right)m/sec.\)

Time = 1 minute = 60 seconds.

Let the length of the tunnel be *x* metres.

Then,\(\left(\frac{800+x}{60}\right) = \frac{65}{3}\)

3(800 + *x*) = 3900

*x* = 500.

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## More Questions on This Topic :

__Question 1.__A train travelling at a speed of 75 mph enters a tunnel \(3^{\frac{1}{2}}\)miles long. The train is\(\frac{1}{4}\)mile

**Options:**

- 2.5 min
- 3 min
- 3.2 min
- 3.5 min

**Answer: Option B**

Total distance covered = \(\left(\frac{7}{2}+\frac{1}{4}\right)miles\)

=\(\frac{15}{4}miles.\)

Thairfor Time taken = \(\left(\frac{15}{4\times75}\right)hrs\)

= \(\frac{1}{20}hrs\)

=\(\left(\frac{1}{20}\times60\right)min.\)

= 3 min.

__Question 2.__A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

**Options:**

- 5 sec
- 6 sec
- 7 sec
- 10 sec

**Answer: Option B**

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

= \(\left(66\times\frac{5}{18}\right)m/sec\)

=\(\left(\frac{55}{3}\right)m/sec.\)

Thairfor Time taken to pass the man = \(\left(100\times\frac{3}{55}\right)sec = 6sec.\)

__Question 3.__Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

**Options:**

- 9
- 9.6
- 10
- 10.8

**Answer: Option D**

Relative speed = (60 + 40) km/hr = \(\left(100\times\frac{5}{18}\right)m/sec=\left(\frac{250}{9}\right)m/sec\)

Distance covered in crossing each other = (140 + 160) m = 300 m.

Required time = \(\left(300\times\frac{9}{250}\right)sec= \frac{54}{5}sec=10.8sec.\)

__Question 4.__A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

**Options:**

- 320 m
- 350 m
- 370 m
- Data inadequate

**Answer: Option B**

Speed = \(\left(\frac{300}{18}\right)m/sec = \frac{50}{3}m/sec.\)

Let the length of the platform be *x* metres.

Then, \(\left(\frac{x+300}{39}\right) = \frac{50}{3}\)

3(*x* + 300) = 1950

*x* = 350 m.

__Question 5.__A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

**Options:**

- 50 m
- 150 m
- 200 m
- Data inadequate

**Answer: Option B**

Let the length of the train be *x* metres and its speed by *y* m/sec.

Then,\(\frac{x}{y} = 15 \Rightarrow y = \frac{x}{15}\)

Thairfor \(\frac{x+100}{25} = \frac{x}{15}\)

15(*x* + 100) = 25*x*

15*x* + 1500 = 25*x*

1500 = 10*x*

*x* = 150 m.

__Question 6.__A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

**Options:**

- 69.5 km/hr
- 70 km/hr
- 79 km/hr
- 79.2 km/hr

**Answer: Option D**

Let the length of the train be *x* metres and its speed by *y* m/sec.

Then, \(\frac{x}{y} = 8 \Rightarrow x = 8y\)

Now,\(\frac{x+264}{20} = y\)

8*y* + 264 = 20*y*

*y* = 22.

Speed = \(22m/sec = \left(22\times\frac{18}{5}\right)km/hr = 79.2 km/hr\)

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