If a train crosses a pole in 30 seconds and a platform of length 100 min 50 seconds, then the length of the train, in meters, is

As per the given condition,
Let the length of the train =x
Let the speed of the train =v m
Hence, $$t=\dfrac{x}{v}$$
$$\Rightarrow \dfrac{x}{v}=30--------(i)$$
Train crosses the platform in$$50=\dfrac{x+100}{v}--------------(ii)$$
From equation (i) and (ii)
$$\Rightarrow \dfrac{30v+100}{v}=50$$
$$\Rightarrow 50v-30v=100$$
$$\Rightarrow 20v=100$$
$$\Rightarrow v=5m/sec$$
So, length of the train $$x=30\times v=30\times 5=150m$$