A train passes two bridges of length 500 metres and 250 metres in 100 seconds and 60 seconds respectively. The length of train is :

Let the length of train be $$l$$ metre
According to the question,
Time = $$\frac{{{\text{Distance}}}}{{{\text{Speed}}}}$$
⇒ 100 =$$\frac{{{\text{500 + }}l}}{{{\text{Speed}}}}$$
⇒ Speed = $$\frac{{500 + l}}{{100}}$$    ..... (i)
Again,
60 = $$\frac{{{\text{250 + }}l}}{{{\text{Speed of Train}}}}$$
Speed = $$\frac{{{\text{250 + }}l}}{{{\text{60}}}}$$    ..... (ii)
Equation (i) and (ii)
$$\eqalign{ & \Rightarrow \frac{{500 + l}}{{100}} = \frac{{250}}{{60}} \cr & \Rightarrow 1500 + 3l = 1250 + 5l \cr & \Rightarrow 2l = 250 \cr & \therefore {\text{Length of train = 125 metres}} \cr} $$