Gumbel 200-year flood from 50 and 100-year floods

Gumbel's equation is linear in the reduced variate: $x_T=a+b\,y_T$, with $y_T=-\ln[\ln(T/(T-1))]$. The two given floods fix the line, so $Y_n$ and $S_n$ are not needed for $x_{200}$ (they are needed only to separate the line into $\bar x$ and $\sigma$).

$$b=\frac{\sigma}{S_n}=\frac{740-660}{4.6001-3.9019}=114.58 \text{ m}^3/\text{s}$$ $$x_{200}=660+114.58\,(5.2958-3.9019)=820 \text{ m}^3/\text{s}$$

(Check with the statistics: $\sigma=b\,S_n=114.58\times1.12843=129.3$ m³/s and $\bar x=660-b(y_{50}-Y_n)=274.8$ m³/s.)

Answer: 200-year flood ≈ 820 m³/s.