A moving train crosses a man standing on a platform and the platform 300 metres long in 10 seconds and 25 seconds respectively. What will be the time taken by the train to cross a platform 200 metre long?

If train crosses the platform i.e. it covers the distance equal to the length of train and platform. In the question train crosses the man who stands on the platform in 10 seconds and crosses the man + platform in 25 seconds i.e. train crosses the platform whose length is 300 metres in 25 - 10 = 15 seconds, here train's length is not added.
So speed of the train $$ = \frac{{300}}{5} \Rightarrow 20\,{\text{m/sec}}$$
Length of the train = 10 × 20 = 200 metres (If train crosses the only man in 10 seconds)
Time taken by the train to cross a platform 200 m long
$$\eqalign{ & = \frac{{{\text{Length of train}} + {\text{Platform}}}}{{{\text{Speed}}}} \cr & = \frac{{200 + 200}}{{20}} \cr & = \frac{{400}}{{20}} \cr & = 20 \cr} $$
Time taken by train = 20 seconds