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Quantitative Aptitude

TRAINS MCQs

Problems On Trains

Total Questions : 842 | Page 5 of 85 pages
Question 41.

How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?

  1.    25
  2.    30
  3.    45
  4.    45
 Discuss Question
Answer: Option B. -> 30

Speed of the train relative to man


= (63 - 3) km/hr


 

= 60 km/hr


\(\left(60\times\frac{5}{18}\right)m/sec\)


=\(\left(\frac{50}{3}\right)m/sec\)


 


Thairfor Time taken to pass the man = \(\left(500\times\frac{3}{50}\right)sec\)


= 30 sec.

Question 42.

Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

  1.    12 sec
  2.    24 sec
  3.    48 sec
  4.    60 sec
 Discuss Question
Answer: Option B. -> 24 sec

Relative speed = \(\left(45+30\right)m/sec\) 


\(\left(75\times\frac{5}{18}\right)m/sec\)


=\(\left(\frac{125}{6}\right)m/sec.\)


We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.


So, distance covered = Length of the slower train.


Therefore, Distance covered = 500 m.


Therefore. = \(\left(500\times\frac{6}{125}\right) = 24sec.\)

Question 43.

Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

  1.    10
  2.    18
  3.    36
  4.    72
 Discuss Question
Answer: Option C. -> 36

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


Then, relative speed of the two trains = 2x m/sec.


So,2x= \(\frac{(120+120)}{12}\)


2x = 20


 x = 10.


Therefor Speed of each train = 10 m/sec = \(\left(10\times\frac{18}{5}\right)km/hr =36 km/hr\)

Question 44.

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

  1.    10
  2.    12
  3.    15
  4.    20
 Discuss Question
Answer: Option B. -> 12

Speed of the first train = \(\left(\frac{120}{10}\right)m/sec = 12m/sec.\)


Speed of the second train =\(\left(\frac{120}{15}\right)m/sec = 8m/sec\)


Relative speed = (12 + 8) = 20 m/sec.


Therefore Required time = \(\left[\frac{(120+120)}{20}\right]sec = 12sec.\)


 

Question 45.

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is:

  1.    48 km/hr
  2.    54 km/hr
  3.    66 km/hr
  4.    82 km/hr
 Discuss Question
Answer: Option D. -> 82 km/hr

Let the speed of the second train be x km/hr.


Relative speed = \(\left(x+50\right)km/hr\)


\(\left[(x+50)\times\frac{5}{18}\right]m/sec\)


=\(\left[\frac{250+5x}{18}\right]m/sec.\)


Distance covered = (108 + 112) = 220 m.


\(\therefore \frac{220}{\left[\frac{250+5x}{18}\right]}=6\)


250 + 5x = 660


 x = 82 km/hr.


 

Question 46.

Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train?

  1.    23 m
  2.    \(23\frac{2}{9}m\)
  3.    \(27\frac{7}{9}m\)
  4.    29m
 Discuss Question
Answer: Option C. -> \(27\frac{7}{9}m\)

Relative speed = (40 - 20) km/hr = \(\left(20\times\frac{5}{18}\right)m/sec=\left(\frac{50}{9}\right)m/sec\)


Therefore  Length of faster train = \(\left(\frac{50}{9}\times5\right)m = \frac{250}{9}m=27\frac{7}{9}\)

Question 47.

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

  1.    45 m
  2.    50 m
  3.    54 m
  4.    72 m
 Discuss Question
Answer: Option B. -> 50 m

2 kmph = \(\left(2\times\frac{5}{18}\right)m/sec= \frac{5}{9}m/sec\)


4 kmph =\(\left(4\times\frac{5}{18}\right)m/sec = \frac{10}{9}m/sec\)


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


Then, \(\left[\frac{x}{y-\frac{5}{9}}\right]=9 and
\left[\frac{x}{y-\frac{10}{9}}\right] = 10\)


Therefore  9y - 5 = x and 10(9y - 10) = 9x


9y - x = 5 and 90y - 9x = 100.


On solving, we get: x = 50.


Therefore Length of the train is 50 m.

Question 48.

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

  1.    66 km/hr
  2.    72 km/hr
  3.    78 km/hr
  4.    81 km/hr
 Discuss Question
Answer: Option D. -> 81 km/hr

4.5 km/hr =\(\left(4.5\times\frac{5}{18}\right)m/sec=\frac{5}{4}m/sec = 1.25m/sec, and\)


5.4 km/hr =\(\left(5.4\times\frac{5}{18}\right)m/sec=\frac{3}{2}m/sec = 1.5m/sec,\)


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


Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5


 8.4x - 10.5 = 8.5x - 12.75


 0.1x = 2.25


 x = 22.5


Speed of the train =\(\left(22.5\times\frac{18}{5}\right)km/hr = 81km/hr.\)

Question 49.

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

  1.    400 m
  2.    450 m
  3.    560 m
  4.    600 m
 Discuss Question
Answer: Option A. -> 400 m

Let the length of the first train be x metres.


Then, the length of the second train is\(\left(\frac{x}{2}\right)metres.\)


Relative speed = (48 + 42) kmph =\(\left(90\times\frac{5}{18}\right)m/sec = 25m/sec\)


\(\frac{[x+(\frac{x}{2})]}{25}=12 or \frac{3x}{2}=300 . or . x= 200\)


Therefore Length of first train = 200 m.


Let the length of platform be y metres.


Speed of the first train = \(\left(48\times\frac{5}{18}\right)m/sec = \frac{40}{3}m/sec\)


\(\therefore\left(200+y\right)\times\frac{3}{40}= 45\)


 600 + 3y = 1800


 y = 400 m.

Question 50.

Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

  1.    9 a.m.
  2.    10 a.m.
  3.    10.30 a.m.
  4.    11 a.m.
 Discuss Question
Answer: Option B. -> 10 a.m.

Suppose they meet x hours after 7 a.m.


Distance covered by A in x hours = 20x km.


Distance covered by B in (x - 1) hours = 25(x - 1) km.


Therefore 20x + 25(x - 1) = 110


 45x = 135


 x = 3.


So, they meet at 10 a.m.

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