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Problems on Trains - General Aptitude

Q1:

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:

A 45 m

B 50 m

C 54 m

D 72 m

ANS:A - 45 m

2 kmph = ( 2 x 5 ( m/sec = 5 m/sec.
18 9
   
4 kmph = ( 4 x 5 ( m/sec = 10 m/sec.
18 9
  Let the length of the train be x metres and its speed by y m/sec.  
Then, ( x ( = 9 and ( x ( = 10.
y - 5
9
y - 10
9
  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.