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Why does the question mention "full load currents", what if there isn't such currents, would the transformer function differently?
What are the full-load primary and secondary currents of a 25000/240-V, 50-kVA transformer? Assume that the 25000-V winding is the primary.
kVA ratings correspond to full load conditions.
By full load is meant the load (obviously, on secondary) which would make transformer transfer it's rated power from primary to secondary. For example when 50 kVA is on full load, it would be transferring 50 kVA from primary to secondary. If primary voltage on full load is 25000 V (as in your case) then primary current should be (50*10^3 / 25000) ampere.
Now coming to your primary question,
if there isn't such currents
means that there isn't such load on secondary that can fully load transformer.
If transformer is under-loaded, primary (and hence secondary) currents would be less than full load values. For e.g. if transformer is on half-load (means load connected at secondary is half the full load), then it would drive exactly half current than full load current. Say your full load current is 'I' ampere then you half load current would be 'I/2' ampere. If transformation ration is 'k', then half-load secondary current would be 'I/2k' ampere.
If transformer is over-loaded, then it may damage winding and/or insulation. However, if we neglect such effect (and you shouldn't neglect it in practice) then, transformer which is on double-load will be drawing twice the full load current in both, primary and secondary winding.
Use basic formula:
$$P = 1.732 \cdot V \cdot I$$ $$I= {P\over(1.732 \cdot V)}$$
For primary H.T:
$$I = {{50 \cdot 1000}\over{(1.732 \cdot 25 \cdot 1000)}} = 1.15A$$
For secondary L.T:
$$I = {{50 \cdot 1000}\over{(1.732 \cdot 240)}}=120A$$
The question is asking what the currents would be at full load. If the load is less than full load, then so too are the currents.
When the transformer is "unloaded" you won't have voltage drops across the windings. These voltage drops are caused by the resistance of the windings, and are a reflection of the current flowing through them. You can expect the output side of a transformer to exhibit a higher no-load voltage than its under-load voltage. I'm speaking generally, there are other causative effects, e.g., transformer efficiency.
