A train travelling at a uniform speed, clears a platform $240\text{ meters}$ long in $10\text{ seconds}$ and passes a telegraph post in $6\text{ seconds}$. Find the length of the train and its speed.

Let the length of the train be $L$ meters and its speed be $v$ m/s.
Case 1: Passing a telegraph post (crosses its own length):

$$\text{Speed}=\frac{\text{Distance}}{\text{Time}}⟹v=\frac{L}{6}⟹L=6v\text{— (Equation 1)}$$

Case 2: Clearing a platform of length $240\text{ m}$:

$$\text{Speed}=\frac{\text{Length of train}+\text{Length of platform}}{\text{Time}}$$

$$v=\frac{L+240}{10}\text{— (Equation 2)}$$

Substitute $L=6v$ from Equation 1 into Equation 2:

$$v=\frac{6v+240}{10}$$

$$10v=6v+240$$

$$4v=240⟹v=60\text{ m/s}$$

Now, find the length of the train ($L$):

$$L=6\times 60=360\text{ meters}$$

Convert speed from m/s to km/hr:

$$\text{Speed}=60\times \frac{18}{5}=12\times 18=216\text{ km/hr}$$

Therefore, the length of the train is $360\text{ m}$ and its speed is $216\text{ km/hr}$.