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6.
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
  • C.
    10
  • B.
    9.6
  • D.
    10.8
  • Answer & Explanation
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Answer : [D]
Explanation :
 

Relative speed = (60 + 40 ) km/hr =

  100 x
5
18
   m/sec =  
250
9
   m/sec.  
 
Distance covered in crossing each other = (140 + 160) m = 300 m
 
Required time =   300 x
9
250
   sec =
54
5
 sec = 10.8 sec.  
 
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7.
A train 800 meters 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:
  • A.
    130
  • C.
    500
  • B.
    360
  • D.
    540
  • Answer & Explanation
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Answer : [C]
Explanation :
 
Speed =   78 x
5
18
   m/sec =  
65
3
   m /sec;    
 
Time = 1 minute = 60 sec.
 
Let the length of the tunnel be x meters.
 
Then,
800 + x
60
=
65
3
 
3(800 + x) = 3900
 
x = 500.    
 
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8.
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
  • C.
    260 m
  • E.
    None of these
  • B.
    240 m
  • D.
    320 m
  • Answer & Explanation
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Answer : [A]
Explanation :
 
Relative speed = (120 + 80) km/hr =   200 x
5
18
   m/sec =  
500
9
   m/sec.  
 
Let the length of the other train be x metres.
 
Then,  
x + 270
9
=
500
9
 
x + 270 = 500
 
x = 230.  
 
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9.
A train overtakes two persons who are waking 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:
  • A.
    45 m
  • C.
    54 m
  • B.
    50 m
  • D.
    72 m
  • Answer & Explanation
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Answer : [B]
Explanation :
 
2 kmph =   2 x
5
18
   m/sec =
5
9
 m/sec and 4 kmph =
10
9
 m/sec.
 
Let the length of the train be x metres and its speed be y m/sec.
 
Then,
 
 
x
  y -
5
9
 
 = 9 and
 
x
  y -
10
9
 
 = 10
 
   
 
 
  9y - 5 = x and 10 (9y - 10) = 9x
 
 9y - x = 5 and 90y - 9x = 100.        
 
On solving, we get : x = 50.
 
 
  Length of the train is 50 m.        
 
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10.
Two trains, one from Howrah to patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
  • A.
    2 : 3
  • C.
    6 : 7
  • B.
    4 : 3
  • D.
    9 : 16
  • Answer & Explanation
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Answer : [B]
Explanation :
 
Let us name the trains as A and B. Then,
 
(A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3        
 
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