The ratio between the speeds of two trains is $7:8$. If the second train runs 400 km in 4 hours, then the speed of the first train is: 

In this question, we are given that the ratio between the speeds of two trains is $7:8$. The second train covers 400 km in 4 hours.
We need to find the speed of the first train.
The speed of the first train is $7x km/h$ and the speed of the second train is $8x km/h$.
We assume that the second train travels 400 km in 4 hours, so we have this:

$$\begin{gathered} 8x=\frac{400}{4}=100 \\ x=\frac{100}{8} \\ x=12.5 \end{gathered}$$

Therefore, speed nof second train is $8\times 12.5 = 100kmph$

and the speed of first train is $7\times 12.5=87.5kmph$

Hence, the correct option is 'D'