A class has 30 students. The mean mark of the 12 boys is 68 and the mean mark of the whole class is 71. What is the mean mark of the 18 girls?

Total marks of the class = $30\times 71=2130$ and total marks of the boys = $12\times 68=816$, so the girls' total is 2130 − 816 = 1314 over 18 students, a mean of 1314 ÷ 18 = 73. The value 74 comes from the shortcut $2\times 71-68$, which is valid only when the two groups are the same size, and 69.5 is just the plain average of 68 and 71.