A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is?
A) 200 m
B) 90 m
C) 120 m
D) 150 m
Answers
Step-by-step explanation:
Let the length of the train be x m .
The train passes the bridge of length 800 m in 100 s .
The train passes the bridge of 400 m in 60 s .
The speed of the train will be same while travelling through both the bridges .
Speed = distance / time .
First case
Distance will be 800 m + x m
⇒ Distance = ( 800 + x ) m
Time given to us is 100 s .
Speed = distance/time
⇒ Speed = ( 800 + x )/100 m/s ------(1)
Second case
Distance will be 400 m + x m
⇒ Distance = ( 400 + x ) m
Time given to us is 60 s .
Speed = distance/time
⇒ Speed = ( 400 + x )/60 m/s -----(2)
From (1) and (2) speed will remain constant :
( 800 + x ) / 100 m/s = ( 400 + x ) / 60 m/s
⇒ ( 800 + x ) / 5 = ( 400 + x ) / 3
⇒ 3 ( 800 + x ) = 5 ( 400 + x )
⇒ 2400 + 3 x = 2000 + 5 x
⇒ 5 x - 3 x = 2400 - 2000
⇒ 2 x = 400
⇒ x = 400 / 2
⇒ x = 200
The length of the train is 200 m .
Option A
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Let length of the train be x m and speed of the train is s kmph.
Speed, s = (x+800)/100 .... (i)
Speed, s = (x+400)/60 .... (ii)
Equating equation (i) and (ii), we get,
✏ (x+800)/100 = (x+400)/60
✏ 5x+200 = 3x+2400;
✏ 2x = 400;
✏ x = 200 m.