First, let's paraphrase the problem to ensure we understand it correctly:
- Initial Sale: Raphael sells 1000 articles without any profit or loss. This means the total revenue from these 1000 articles equals the total cost price for these articles.
- Additional Sales: He sells the remaining articles (let's denote this number as $n$ ) at an extra cost of $\$ 0.5$ per article. This implies that each of these $n$ articles is sold at a price that is $\$ 0.5$ more than its cost price.
- Total Profit: The total profit from selling these $n$ articles at the increased price is $\$ \mathrm{P}$.
- Question: We need to find out how many additional articles ( $n$ ) Raphael sold, given that the price of each article was the same initially.

Defining Variables
Let's define some variables to model the situation:
1. Let $C$ be the cost price per article.
2. Let $S$ be the selling price per article for the first 1000 articles.

Given that the first 1000 articles are sold without profit or loss:
Total Revenue from first 1000 = Total Cost of first 1000

$$
\(\begin{gathered}
1000 \times S=1000 \times C \\
S=C
\end{gathered}\)
$$


This tells us that the selling price per article for the first 1000 is equal to the cost price, hence no profit or loss.


Additional Sales

For the remaining $n$ articles:
- Each is sold at an extra $\$ 0.5$, so the selling price per article is $S+0.5=C+0.5$.

The profit per additional article is:

$$
\(\text { Selling Price }- \text { Cost Price }=(C+0.5)-C=0.5\)
$$


Total profit from $n$ additional articles:

$$
\(\begin{gathered}
n \times 0.5=P \\
n=\frac{P}{0.5} \\
n=2 P
\end{gathered}\)
$$


Total Articles Sold
The problem mentions "rest of the articles," implying that there are more articles beyond the initial 1000. However, the total number of articles isn't specified, and the question seems to ask for the number of additional articles sold at the higher price, which we've found to be $2 P$.

But looking at the options:
(A) $P+500$
(B) $2 P+1000$
(C) $5 P+1000$
(D) 2000
(E) 5000

Our calculation gives $n=2 P$, but this isn't directly among the options. This suggests that the question might be asking for the total number of articles sold, not just the additional ones.

Verifying Option (B)
If total articles sold $=1000+2 P$, then:
- First 1000: sold at $C$, no profit.
- Next $2 P$ : sold at $C+0.5$, profit $=2 P \times 0.5=P$.

This fits the given information perfectly.
Checking Other Options
- (A) $P+500$ : Doesn't match our calculation.
- (C) $5 P+1000$ : Doesn't match.
- (D) 2000: Constant, doesn't involve $P$.
- (E) 5000: Constant, doesn't involve $P$.

Only (B) fits.
Final Answer
After carefully analyzing the problem and considering the options, the correct answer is:
B