In a frequency table whose classes all have width 5, the cumulative frequency up to the end of the class 25-30 is exactly n/2. What is the median?

Exactly half the observations lie below 30. Treating 30-35 as the median class gives $l=30$ and $cf=\frac{n}{2}$, so Median = $30+\left(\frac{n/2-n/2}{f}\right)\times 5=30$; treating 25-30 as the median class gives $25+\left(\frac{f}{f}\right)\times 5=30$ as well. 25 is the lower boundary of 25-30 and 27.5 is its class mark — neither is the median. The frequency of the next class is not needed, because the numerator $\frac{n}{2}-cf$ is zero whatever $f$ may be.