We present the results of a ROSAT XRT/PSPC observation of a field near the North Galactic Pole containing the interacting galaxy pair NGC 4725/4747. A tidal H I plume emanating from NGC 4747 and also the extended H I disc in NGC 4725 represent 'foreground' screens which will, in principle, cast shadows on any extra-galactic component of the soft X-ray background. The failure to detect such shadowing in the ROSAT observation leads to a 95 per cent upper limit on the intensity of the unresolved extragalactic background of 26.5 keV cm-2 s-1 sr-1 keV-1 at 0.25 keV, after excluding discrete sources brighter than 1.7 x 10(-14) erg cm-1 s-1 in the 0.5-2 keV band. This upper limit increases by a factor of approximately 1.5 if we allow for possible additional line-of-sight absorption associated with a partially ionized component of the high-latitude interstellar medium. These measurements, together with constraints at approximately 1 keV derived from an analysis of the PSPC background spectrum, demonstrate that the extragalactic background between 0.2 and 1 keV has an energy index alpha less than or similar 0.7 (or alpha less than or similar to 1.0 if the more conservative 0.25-keV upper limit applies). We briefly discuss the implications of these results for the source populations that may give rise to the X-ray background radiation.