The ratio of the speeds of two trains is 2 : 7. If the first train runs 250 km in 5 hours, then the sum of the speeds (in km/h) of both the trains is:

The correct answer is 225.

To find the sum of the speeds of both trains, we can break the problem down into simple steps:

Step 1: Find the speed of the first train
We are given that the first train runs 250 km in 5 hours.
Using the formula for speed:
$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
Substituting the given values:
${\text{Speed}}_1=\frac{250\text{ km}}{5\text{ hours}}=50\text{ km/h}$

Step 2: Understand the ratio of the speeds
The ratio of the speeds of the two trains is given as 2 : 7.
Let the speed of the first train be $2x$ and the speed of the second train be $7x$, where $x$ is a common constant ratio factor.

Step 3: Solve for the value of $x$
Since the speed of the first train is 50 km/h, we can set up the following equation:
$2x=50$
Dividing both sides by 2:
$x=25$

Step 4: Calculate the sum of the speeds of both trains
The sum of the speeds of both trains is:
$\text{Sum of speeds}=2x+7x=9x$
Substitute the value of $x$ into the equation:
$\text{Sum of speeds}=9\times 25=225\text{ km/h}$

Therefore, the sum of the speeds of both trains is 225 km/h.