aptitude : : problems on trains
 
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   Exercise 2
   Exercise 1
1.
A train speeds past a pole in 15 seconds and speeds past a platform 100 meters long in 25 seconds. Its length in meters is:
 
A.
150 m

B.

180 m
C.
200 m
D.
140 m
   
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Answer: A
Explanation :
Let the length of the train= x m
Then, speed of the train = x/15 = x+100 / 25
or, 25x = 15x + 1500  or, 10x = 1500
Therefore x= 150 m 






 
2.
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 km per hour speed. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 km per hour. At what time will they meet?
 
A.
10 a.m.

B.

10 p.m.
C.
9 a.m.
D.
8 a.m.
   
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Answer: A
Explanation :
Till 8 a.m., the train from A covers a distance of 20 km. Now, the remaining distance
110 - 20 = 90 km is covered by the trains with relative speed: 20 + 25= 45 km/hr
 
Therefore they meet after = 90/45= 2 hrs. That is, at 8+2 = 10 a.m.






 
3.
Two trains, each 80 m long, pass each other on parallel lines. lf they are going in the same direction, the faster one takes one minute to pass the other completely. If they are going in different directions, they completely pass each other in 3 seconds. Find the rate of each train in m per second.
 
A.
89 and 80 km/hr

B.

78.2 and 90.1 km/hr
C.
110 and 120 km/hr
D.
100.8 and 91.2 km/hr
   
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Answer: D
Explanation :
R1 = 80+80/60 = 160 / 60 = 8/3 m/s 
R2 = 80+80/ 3 = 160 /3 m/s
Speed of the faster train = (8/3)+ (160/3) / 2 = 168/6 = 84/3 m/s
                                            =  84/3 X 18/5 = 100.8 km/hr
Speed of the slower train = (160/3) - (8/3) / 2 = 152/6 m/s = 152/6 X 18/5 = 91.2 km/hr 






 
4.
Two trains measuring 100 and 80 m respectively, run on parallel lines of rails. When travelling in opposite directions they are observed to pass each other in 9 seconds,   but  when they are running in the same direction at the same rates as before, the faster train passes the other in 18 seconds. Find the speed of the two trains in km per hour. 
 
A.
5 and 10 m/s

B.

10 and 15 m/s
C.
15 and 5 m/s
D.
20 and 25 m/s
   
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Answer: C
Explanation :

R1 = Relative speed, when they are moving in the same direction

      =  100 + 80 / 18 = 10 m/s 

R2 = Relative speed, when they are moving in opposite directions

    = 100 +80 / 9 = 20 m/s 

Speed of the faster train  = R1 + R2 / 2 = 10 + 20 / 2 = 15 m/s 

      = 15 X 18 / 5 = 54 km/hr 

Speed of the slower train = R2 - R1 /2 = 20 -10 /2 = 5 m/s

   = 5 X 18 / 5 = 18 km/hr

 

 

 

 

 







 
5.
Two trains running at the rates of 45 and 36 km an hour respectively, on parallel rails in opposite directions, are observed to pass each other in 8 seconds, and when they are running in the same direction at the same rate as before, a person sitting in the faster train observes that he passes the other in 30 seconds. Find the lengths of the trains.
 
A.
70 and 120 m

B.

60 and 110 m
C.
65 and 100 m
D.
75 and 105 m
   
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Answer: D
Explanation :
Relative speed of  two trains= 45 + 36=81 km/hr( when two trains are moving in opposite directions)
 
= 81 X 5/18 = 45/2 = 22(1/2) m/s
 
Therefore length of both the trains = 45/2 X 8 = 180 m
 
Now, when two trains are moving in the same direction, the relative speed
 
= 45- 36 = 9  km/hr = 9X5/18 = 5/2 m/s 
 
The man sitting in the faster train passes the length of the slower train in 30 seconds
Therefore length of the slower train = 5/2 X 30 = 75 m
Therefore length of the faster train = 180 - 75 = 105 m






 
6.
A train 75 metres long overtook a person who was walking at the rate of 6 km an hour, and passed him in 7 (1/2) seconds. Subsequently it  overtook a second person,and passed him in 6 (3/4)  seconds. At what rate was the second person travelling?
 
A.
1 km/hr

B.

2 km/hr
C.
5 km/hr
D.
6 km/hr
   
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Answer: B
Explanation :

Relative speed of the train and first person

75 / (15/2) = 10 m/s 

= 10X 18/5 = 36 km/hr

Therefore speed of the train = 36 + 6 = 42 km/hr 

Now, relative speed of the train and 2nd person 

= 75/27 X4 m/s = 300/27 X18/5 = 40 km/hr

Therefore speed of 2nd person = 42 - 40 = 2 km/hr  







 
7.
How many seconds will a train 60 m in length, travelling at the rate of 42 km an hour,
take to pass another train 84 m long, proceeding in the same direction at the rate of 30 km an hour?
 
A.
40 seconds

B.

44 seconds
C.
43 seconds
D.
43.2 seconds
   
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Answer: D
Explanation :
Relative speed = 42-  30 = 12 km/hr =12 X 5/18 = 10/3 m/s
Time = Total length of both the trains / Relative speed = 84 + 60 / (10/3)    
= 144X3/10 = 43.2 seconds






 
8.
Find the length of a bridge which a train 130 m long, travelling at 45 km an hour, can cross in 30 secs.
 
A.
250 m

B.

255 m
C.
240 m
D.
245 m
   
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Answer: D
Explanation :
45 km/hr = 45 X 5/18 = 25/2 = 12.5 m/s 
Distance covered by the train in 30 seconds = 12.5 X 30 = 375 m
Therefore length of the bridge = 375 - 130 = 245 m 






 
9.
A train travelling at 30 km an hour took 13(1/2)sec in passing a certain point. Find the length of the train.
 
A.
113.5 m

B.

112.5 m
C.
115 m
D.
113 m
   
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Answer: B
Explanation :
30km/hr = 30X5/18 =25/3 m/s 
 
Length of the train = 25/3 X 27/2 = 225/2 = 112.5 m 






 
10.
How long will a train 60 m long travelling at 40 km an hour take to pass through a station whose platform is 90 m long?
 
A.
12 seconds

B.

13 seconds
C.
13.5 seconds
D.
14.5 seconds
   
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Answer: C
Explanation :
speed = 40 km/hr = 40X5/18 m/s
 
Therefore Time = (60+90)/(40X5) X 18 = 150X18/40X5 = 13.5 seconds






 

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