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:

Solution (By Examveda Team)

1^st Method:
Let length of the train be x m and speed of the train is s kmph.
Speed, s = $$\frac{{x + 800}}{{100}}$$ . . . . . (i)
Speed, s = $$\frac{{x + 400}}{{60}}$$ . . . . . (ii)
Equating equation (i) and (ii), we get,
Or, $$\frac{{x + 800}}{{100}}$$  = $$\frac{{x + 400}}{{60}}$$
Or, 5x + 200 = 3x + 2400
Or, 2x = 400
Or, x = 200m

2^nd Method:
As in both cases, the speed of the train is constant, and then we have;
Time α distance
$$\eqalign{ & \frac{{100}}{{60}} = \frac{{x + 800}}{{x + 400}} \cr & {\text{or,}}\,\,x = 200{\text{m}} \cr} $$