250/500 V transformer, parameters both sides

Data as printed: the OC test is on the HV winding (250 V, 1 A, 80 W) and the SC test is on the LV winding (20 V, 12 A, 100 W). The test values are used exactly as given. The transformer is 250/500 V, so the LV winding is 250 V, the HV winding is 500 V, and $K = 2$, $K^2 = 4$.

Open-circuit test (HV side)

$$\begin{aligned} \cos\phi_0 &= \frac{80}{250\times1} = 0.32,\quad I_w = 0.32\ \text{A},\quad I_\mu = \sqrt{1 - 0.32^2} = 0.9474\ \text{A} \\ R_{0H} &= \frac{250}{0.32} = 781.25\ \Omega,\qquad X_{0H} = \frac{250}{0.9474} = 263.9\ \Omega \end{aligned}$$

Short-circuit test (LV side)

$$\begin{aligned} Z_{eq,L} &= \frac{20}{12} = 1.667\ \Omega,\qquad R_{eq,L} = \frac{100}{12^2} = 0.6944\ \Omega \\ X_{eq,L} &= \sqrt{1.667^2 - 0.6944^2} = 1.515\ \Omega \end{aligned}$$

Referred to the high-voltage (HV) side

Impedance moves from LV to HV by multiplying by $K^2 = 4$:

$$R_{eq,H} = 4\times0.6944 = 2.778\ \Omega,\qquad X_{eq,H} = 4\times1.515 = 6.060\ \Omega$$

with shunt branch $R_{0H} = 781.25\ \Omega$, $X_{0H} = 263.9\ \Omega$.

  HV side:  Req=2.778 ohm  Xeq=6.06 ohm
 o--+-----/\/\/\-----UUUU------o
    |
   [R0=781.25] [X0=263.9]   Load
    |
 o--+---------------------------o

Referred to the low-voltage (LV) side

Shunt branch is divided by $K^2$:

$$R_{0L} = \frac{781.25}{4} = 195.3\ \Omega,\qquad X_{0L} = \frac{263.9}{4} = 65.97\ \Omega$$

with series branch $R_{eq,L} = 0.6944\ \Omega$, $X_{eq,L} = 1.515\ \Omega$.

  LV side:  Req=0.694 ohm  Xeq=1.515 ohm
 o--+-----/\/\/\-----UUUU------o
    |
   [R0=195.3] [X0=65.97]   Load
    |
 o--+---------------------------o

Answer: HV side: $R_0 = 781.25\ \Omega$, $X_0 = 263.9\ \Omega$, $R_{eq} = 2.778\ \Omega$, $X_{eq} = 6.060\ \Omega$. LV side: $R_0 = 195.3\ \Omega$, $X_0 = 65.97\ \Omega$, $R_{eq} = 0.694\ \Omega$, $X_{eq} = 1.515\ \Omega$

Note: 250 V is the LV rating, so the side labels in the paper are probably swapped (normally the OC test is done on the LV side and the SC test on the HV side). With that reading the results are: LV side $R_0 = 781.25\ \Omega$, $X_0 = 263.9\ \Omega$, $R_{eq} = 0.1736\ \Omega$, $X_{eq} = 0.3788\ \Omega$; HV side $R_0 = 3125\ \Omega$, $X_0 = 1055.5\ \Omega$, $R_{eq} = 0.6944\ \Omega$, $X_{eq} = 1.515\ \Omega$.