To calculate the average marks in mathematics of the class, we will use the weighted average method.
Weighted Average = (weight1 × value1) + (weight2 × value2) + (weight3 × value3)……
Weighted Average = (Total weight × Total value)

Let us consider the following data:
Division 1: Number of students = 30 and Average marks in mathematics = 40%
Division 2: Number of students = 40 and Average marks in mathematics = 30%
Division 3: Number of students = 30 and Average marks in mathematics = 50%

Total number of students = 30 + 40 + 30 = 100

We will calculate the total weight and total value of the class using the following formula:

Total Weight = (Number of students in Division 1 × Average marks in mathematics of Division 1) + (Number of students in Division 2 × Average marks in mathematics of Division 2) + (Number of students in Division 3 × Average marks in mathematics of Division 3)
Total Weight = (30 × 40) + (40 × 30) + (30 × 50)
Total Weight = 1200

Total Value = (Average marks in mathematics of Division 1 × Number of students in Division 1) + (Average marks in mathematics of Division 2 × Number of students in Division 2) + (Average marks in mathematics of Division 3 × Number of students in Division 3)
Total Value = (40 × 30) + (30 × 40) + (50 × 30)
Total Value = 1500

Now, we will calculate the average marks in mathematics of the class using the weighted average formula:
Weighted Average = (Total weight × Total value)
Weighted Average = (1200 × 1500)
Weighted Average = 1800000

Average marks in mathematics of the class = (Weighted Average ÷ Total number of students)
Average marks in mathematics of the class = (1800000 ÷ 100)
Average marks in mathematics of the class = 39%

Hence, the average marks in mathematics of the class is 39%. Therefore, the correct answer is Option B 39%.

Explanation:
The weighted average method is used to calculate the average of a set of values when each value has a different weight or importance. The weighted average formula is used to calculate the average of a set of values when each value has a different weight or importance. In the given problem, the total weight and total value of the class are calculated using the weighted average formula and then the average marks in mathematics of the class is calculated using the formula.

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