The ratio between the speeds of two trains is 7 : 5. If the second train runs 400 km in 4 h, then the speed of the first train is:

Correct option is A

Given:

The ratio of the speeds of two trains is 7 : 5.

The second train runs 400 km in 4 hours.

Formula Used:

​$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$​​

Solution:

The second train covers 400 km in 4 hours, so its speed is:

​$$\text{Speed of second train} = \frac{400 \, \text{km}}{4 \, \text{hours}} = 100 \, \text{km/h}$$​​

The ratio of the speeds of the first train to the second train is given as 7 : 5.
Let the speed of the first train be 7x and the speed of the second train be 5x.
We know the speed of the second train is 100 km/h, so:

5x = 100

x = $$\frac{100}{5} = 20$$​

The speed of the first train is 7x:

7x$$= 7 \times 20 = 140 \, \text{km/h}$$​

The speed of the first train is 140 km/h.