Correct Answer  Option 1 : 508 W and 542 W
Concept:
Hysteresis losses: These are due to the reversal of magnetization in the transformer core whenever it is subjected to the alternating nature of magnetizing force.
\({W_h} = \eta B_{max}^{1.6}fv\)
\({B_{max}} \propto \frac{V}{f}\)
Where
x is the Steinmetz constant
Bm = maximum flux density
f = frequency of magnetization or supply frequency
v = volume of the core
At a constant V/f ratio, hysteresis losses are directly proportional to the frequency.
Wh ∝ f
Eddy current losses: Eddy current loss in the transformer is I2R loss present in the core due to the production of eddy current.
\({W_e} = K{f^2}B_m^2{t^2}V\)
\({B_{max}} \propto \frac{V}{f}\)
Where,
K  coefficient of eddy current. Its value depends upon the nature of magnetic material
Bm  Maximum value of flux density in Wb/m2
t  Thickness of lamination in meters
f  Frequency of reversal of the magnetic field in Hz
V  Volume of magnetic material in m3
At a constant V/f ratio, eddy current losses are directly proportional to the square of the frequency.
We ∝ f2
Iron losses or core losses or constant losses are the sums of both hysteresis and eddy current losses.
Wi = Wh + We
At constant V/f ratio, Wi = Af + Bf2
\({230 \over50} = {138 \over30}=4.6 \;(Constant \;{V\over f})\)
Calculation:
The table below shows the given data.

Frequency

Core losses

Case 1

50 Hz

1050 W

Case 2

30 Hz

500 W

Case 3

50 Hz

W_{h} , W_{e}?

Now, the equations for Case 1 and Case 2 are given below
Case 1: 1050 = A (50) + B (50)2
Case 2: 500 = A (30) + B (30)2
By solving the above two equations,
A = 10.1667, B = 0.2166
Case 3: Hysteresis losses (Wh) = Af = 10.1667 × 50 = 508 W
Eddy current losses (We) = Bf2 = 0.2166 × (50)2 = 542 W