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Quantitative Aptitude

TRAINS MCQs

Problems On Trains

Total Questions : 842 | Page 4 of 85 pages
Question 31.

A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

  1.    230m
  2.    240m
  3.    260m
  4.    320m
  5.    None of these
 Discuss Question
Answer: Option A. -> 230m

Relative speed = (120 + 80) km/hr


=\(\left(200\times\frac{5}{18}\right)m/sec\)


=\(\left(\frac{500}{9}\right)m/sec\)


Let the length of the other train be x metres.


Then,\(\frac{x+270}{9}=\frac{500}{9}\)


x + 270 = 500


 x = 230.

Question 32.

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

  1.    230m
  2.    240m
  3.    260m
  4.    270m
 Discuss Question
Answer: Option D. -> 270m

Speed =\(\left(72\times\frac{5}{18}\right)m/sec=20m/sec\)


Time = 26 sec.


Let the length of the train be x metres.


Then, \(\frac{x+250}{26} = 20\)


x + 250 = 520


 x = 270.

Question 33.

Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

  1.    30 km/hr
  2.    45 km/hr
  3.    60 km/hr
  4.    75 km/hr
 Discuss Question
Answer: Option C. -> 60 km/hr

Let the speed of the slower train be x m/sec.


Then, speed of the faster train = 2x m/sec.


Relative speed = (x + 2x) m/sec = 3x m/sec.


\(\left(\frac{100+100}{8}\right) = 3x\)


24x = 200


x=\(\frac{25}{3}.\)


So, speed of the faster train = \(\frac{50}{3}m/sec\)


\(\left(\frac{50}{3}\times\frac{18}{5}\right)km /hr\)


   = 60 km/hr.

Question 34.

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:

  1.    9
  2.    9.6
  3.    10
  4.    10.8
 Discuss Question
Answer: Option D. -> 10.8

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 35.

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?

  1.    5 sec
  2.    6 sec
  3.    7 sec
  4.    10 sec
 Discuss Question
Answer: Option B. -> 6 sec

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 36.

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

  1.    2.5 min
  2.    3 min
  3.    3.2 min
  4.    3.5 min
 Discuss Question
Answer: Option B. -> 3 min

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 37.

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:

  1.    130
  2.    360
  3.    500
  4.    540
 Discuss Question
Answer: Option C. -> 500

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.

Question 38.

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?

  1.    320 m
  2.    350 m
  3.    370 m
  4.    Data inadequate
 Discuss Question
Answer: Option B. -> 350 m

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 39.

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

  1.    50 m
  2.    150 m
  3.    200 m
  4.    Data inadequate
 Discuss Question
Answer: Option B. -> 150 m

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) = 25x


 15x + 1500 = 25x


 1500 = 10x


 x = 150 m.

Question 40.

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?

  1.    69.5 km/hr
  2.    70 km/hr
  3.    79 km/hr
  4.    79.2 km/hr
 Discuss Question
Answer: Option D. -> 79.2 km/hr

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


 8y + 264 = 20y


 y = 22.


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

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