A train is moving in from north to south direction. It overtakes Raj and Madhur who are walking in the same direction at the rate of 2 km/h and 4 km/h in 9 sec and 10 sec, respectively. If the train is x meters long, find the value of x.

Correct option is C

Given:

Walking speeds: $$2 \, \text{km/h}, 4 \, \text{km/h}$$​

Times: $$9 \,\text{sec}, 10 \, \text{sec}.$$​

Formula Used:

Relative speed = $$(\text{Train speed} - \text{Walking speed}) \times \frac{1000}{3600}$$​

Train's length: 

$$x = \text{Relative speed} \times \text{Time}$$​

Solution:
For first person:

$$x = \left( v - 2 \right) \times \frac{1000}{3600} \times 9$$​​

For second person:

$$x = \left( v - 4 \right) \times \frac{1000}{3600} \times 10$$​​

Equating the equation and simplifying:

$$9(v - 2) = 10(v - 4) \\ \ \\ \Rightarrow \quad v = 22 \, \text{km/h}$$ 

Now, Finding x:

$$x = \left( 22 - 2 \right) \times \frac{1000}{3600} \times 9 = 50 \, \text{meters}$$

Thus, the train length is 50 meters.