A bus travels from Kolkata to Digha at the rate of $55\text{km/hour}$ and returns at the rate of $66\text{km/hour}$. Then the average rate of the whole journey is:

When an object covers the exact same distance at two different speeds, say $v_1$ and $v_2$, the average speed for the entire journey is given by the harmonic mean formula:
$$\text{Average Speed}=\frac{2v_1{v}_2}{v_1+v_2}$$

Given:

* $v_1=55\text{km/hour}$
* $v_2=66\text{km/hour}$

Substitute these values into our formula:

$$\text{Average Speed}=\frac{2\times 55\times 66}{55+66}$$

$$\text{Average Speed}=\frac{2\times 55\times 66}{121}$$

Notice that $121=11\times 11$, so we can simplify the expression:

$$\text{Average Speed}=\frac{2\times (55/11)\times (66/11)}{1}=2\times 5\times 6=60\text{km/hour}$$