4. The numbers $x_{1}, x_{2}, \cdots, x_{100}$ satisfy the following conditions: For $k=1,2, \cdots, 100, x_{k}$ is less than the sum of the other 99 numbers by $k$. Then the value of $x_{25}$ is $\qquad$ .
4. $\frac{650}{49}$.

Let $S=x_{1}+x_{2}+\cdots+x_{100}$, then
$$
x_{k}=\left(S-x_{k}\right)-k(k=1,2, \cdots, 100) \text {, }
$$

i.e., $k+2 x_{k}=S$.
Summing over $k$ gives
$$
\begin{array}{l}
(1+2+\cdots+100)+2 S=100 S \\
\Rightarrow S=\frac{2525}{49} \\
\Rightarrow x_{25}=\frac{S-25}{2}=\frac{650}{49} .
\end{array}
$$