Out of $15$ cows, one worth $\text{Rs. }1800$ was removed and a horse was taken in. If their average price is thereby increased by $\text{Rs. }300$, then the price of the horse is

Let the price of the horse be $H$.
The total number of animals remains unchanged at $15$.

The net increase in the total value of all animals combined is:

$$\text{Net Increase}=\text{Number of items}\times \text{Increase in Average}=15\times 300=\text{Rs. }4500$$

The difference in value between the incoming horse and the outgoing cow accounts entirely for this total increase:

$$H-1800=4500$$

$$H=4500+1800=\text{Rs. }6300$$