Train A travelling at 81 kmph overtakes another train B, 230 metre long and completely passses it in

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27 May 2022 Time Distance & Speed

Train A travelling at 81 kmph overtakes another train B, 230 metre long and completely passses it in 104 seconds. If the trains had been going in opposite directions, they would have passed each other in 13 seconds. The length (in metre) of A and the speed (in Kmph) of B are respectively

OPtion

1) 210 ; 42
2) 290 ; 35
3) 320 ; 35
4) 290 ; 17.5
5) 275 ; 42
6) 320 ; 63
7) 245 ; 35
8) 290 ; 63
9) 290 ; 42
10) None of these

Solution

Speed of train A = 81 kmph = 81*5/18 = 45/2 m/s. Let the speed of train B = x m/s
Relative speed in same direction=(45/2 - x) m/s
If the length of train A be 'y' metres, then time taken to cross in same direction = (y+230)/(45/2 - x) = 104 sec.
⇒ 104x + y = 2110 ---(i)
Relative speed in opposite direction=(45/2 + x) m/s
Time taken to cross in opposite direction = (y+230)/(45/2 + x) = 13 sec.
⇒ 26x - 2y = -125 ---(i)
Solving eqn. (i) & (ii), we get x=17.5 , y=290
Speed of train B in kmph = 17.5*18/5 = 63 kmph.

Correct Option: 8 Best Solution (1)

G.S.Kantharao   2 years AGO

Length and speed of A and B are =X,Y
Relative Lengths =X+230
Relative speeds per second=(81+Y)5/18,(81-Y)5/18
Now d/s=t
(230+X)18/5(81-Y)=104
=>(230+X)18=520(81-Y)
=>4140+18X
=42120-520Y
=>18X+520Y=37980--(1)
18(230+X)/5(81+Y)=13
4140+18X=5265+65Y
18X-65Y=1125--(2)
(1)--(2)=585y=36855
Y=63Kmph
18X=1125+65*63=5220
X= 290m
So my option is 8👈

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