Discussion
The average marks of 30 students of section A of class X is 70. Whereas, the average marks of 40 students of section B of class X is 80. What is the average marks for both sections combined together?
Answer: B
The combined average is \(75\frac{5}{7}\). The total marks are the sum of the two sections' totals, divided by the total number of students.
\[ 30 \times 70 + 40 \times 80 = 2100 + 3200 = 5300 \]\[ \frac{5300}{70} = 75\frac{5}{7} \]Since 70 times 75 is 5250 and the remaining 50 gives \(\frac{50}{70} = \frac{5}{7}\), the options with 74, 76 or 77 as the whole part do not equal 5300 divided by 70.
A weighted average is used because the sections have different sizes. A simple average of 70 and 80 would give 75, but section B has more students (40 against 30), so the combined mean is pulled above 75, to \(75\frac{5}{7}\), which is the first check that option A, 74 5/7, cannot be right.
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