A test was written by a class whose marks are grouped as 0-10: 5, 10-20: 18, 20-30: 15, 30-40: f, 40-50: 6, and the mean mark is 25. How many students wrote the test altogether?

Class marks 5, 15, 25, 35, 45 give $\sum f_i{x}_i=940+35f$ and $\sum f_i=44+f$. From $\frac{940+35f}{44+f}=25:1100+25f=940+35f$, so $10f=160$ and $f=16$. The question asks for the TOTAL, which is 44 + 16 = 60 students. "16" is $f$ itself, not the total; "44" is the total of the four known frequencies; "160" is $10f$ left undivided.