A cow was standing on a bridge, Sm away from the middle of the bridge. A train was coming towards the bridge from the ends nearest to the cow. Seeing this, cow ran towards the train and managed to escape when the train was 2m away from bridge. If it had run in the opposite direction, it would hit by the train 2m before the end of the bridge. What is the length of the bridge in meters assuming the speed of the train is 4 times that of cow?

Let, the distance of cow from the nearest end of bridge is x meters

$\therefore$Half length of the bridge is (x + 5)  meters

Now, assume that, the cow runs x meters in y seconds.

$\therefore$The train covers in y seconds = 4x meters.

Given, that the train was (4x + 2) meters away from the bridge when the cow saw the train.

Here, covering time of = x + 10 - 2 = (x + 8) meters distance by the cow is same covering time of

(4x + 2 + 2x + 10 - 2) = (6x + 10) meters distance covered by train.

Here, (x + 10) = Distance of cow from the far end to hit the cow.

( 4x +2)= Distance covered by the train to reach at the near end.

And (2x + 10 - 2) = Distance covered by train from near end.

$\therefore$ We can write, 4(x + 8) = 6x + 10

= 4x + 32 = 6x + 10

= 2x = 22

$\therefore$x = 11

$\therefore$ Length of the bridge = 2x+10= (2 x 11)+10=22+ 10 = 32 meters.