The average weight of P and his four friends is $52.4\text{kg}$. If P is $3\text{kg}$ lighter than the average weight of his four friends, then what is the weight of P (in $\text{kg}$)?

Let the average weight of P's four friends be $W$.
The total weight of the four friends $=4W$.

According to the question, P is $3\text{kg}$ lighter than the average weight of his four friends:
$$\text{Weight of P}=W-3$$

The average weight of P and his four friends together (total $5$ people) is given as $52.4\text{kg}$:
$$\frac{\text{Weight of P}+\text{Total weight of four friends}}{5}=52.4$$
$$\frac{(W-3)+4W}{5}=52.4$$
$$5W-3=52.4\times 5$$
$$5W-3=262$$
$$5W=265⟹W=53$$

Now, substitute $W=53$ to find the weight of P:
$$\text{Weight of P}=53-3=50\text{kg}$$