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Arithmetic Aptitude | Problems on Trains 4 - with Explanation


1. 
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?
A.230 m
B.240 m
C.260 m
D.320 m
E.None of these
Answer: Option A
Explanation:
Relative speed = (120 + 80) km/hr
   =200 x5m/sec
18
   =500m/sec.
9
Let the length of the other train be x metres.
Then,x + 270=500
99
 x + 270 = 500
 x = 230.


2. 
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?
A.230 m
B.240 m
C.260 m
D.270 m
Answer: Option D
Explanation:
Speed =72 x5m/sec= 20 m/sec.
18
Time = 26 sec.
Let the length of the train be x metres.
Then,x + 250= 20
26
 x + 250 = 520
 x = 520-250=270

3. 
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:
A.30 km/hr
B.45 km/hr
C.60 km/hr
D.75 km/hr
Answer: Option C
Explanation:
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.
(100 + 100)= 3x
8
 24x = 200
 x =25.
3
So, speed of the faster train =50m/sec
3
   =50x18km/hr
35
   = 60 km/hr.


4.
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:
A.9
B.9.6
C.10
D.10.8
Answer: Option D
Explanation:
Relative speed = (60 + 40) km/hr =100 x5m/sec=250m/sec.
189
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time =300 x9sec=54sec = 10.8 sec.
2505


5.
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?
A.5 sec
B.6 sec
C.7 sec
D.10 sec
Answer: Option B
Explanation:
Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.
   =66 x5m/sec
18
   =55m/sec.
3
 Time taken to pass the man =110 x3sec = 6 sec.
55

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