, 2004

Digital images consist of a very large number of equally spaced dots called pixels. The resolution of an image is the number of pixels/cm in each of the horizontal and vertical directions. Thus, an image with dimensions $10$ cm by $15$ cm and a resolution of $75$ pixels/cm has a total of $(10\times75)\times(15\times75)=843\,750$ pixels. If each of these dimensions was increased by $n\%$ and the resolution was decreased by $n\%$, the image would have $345\,600$ pixels. Determine the value of $n$.