If the average marks of the 1/4th class is 85% and that of 1/3rd class is 70% and the average marks of the rest class is 56% then the average of the whole class is (for the given subjects):

Options

A. 0.67916
B. 0.7233
C. 0.69165
D. can't be determined

Answer

To find the average marks of the whole class, we need to consider the average marks of each section of the class and the number of students in each section. Let's assume the total number of students in the whole class is 1 (for simplicity), and we will denote the fractions of the class as follows:

- Let the total number of students in the class be 1.
- The fraction of students in the 1/4th class is 1/4.
- The fraction of students in the 1/3rd class is 1/3.
- The remaining fraction of students in the rest of the class can be calculated as follows:

1. Calculate the fraction of the rest of the class:
\[ \text{Rest of the class} = 1 - \left(\frac{1}{4} + \frac{1}{3}\right) \]

To add the fractions, we need a common denominator. The least common multiple of 4 and 3 is 12. Thus, we convert the fractions:
\[ \frac{1}{4} = \frac{3}{12}, \quad \frac{1}{3} = \frac{4}{12} \]
Therefore:
\[ \frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12} \]
So, the fraction of the rest of the class is:
\[ 1 - \frac{7}{12} = \frac{5}{12} \]

2. Now, we have the fractions of each class:
- 1/4th class: 85% average
- 1/3rd class: 70% average
- Rest class: 56% average

3. Calculate the weighted average of the whole class:
\[ \text{Average} = \left(\frac{1}{4} \times 85\right) + \left(\frac{1}{3} \times 70\right) + \left(\frac{5}{12} \times 56\right) \]

Let's calculate each term:
- For the 1/4th class:
\[ \frac{1}{4} \times 85 = \frac{85}{4} = 21.25 \]
- For the 1/3rd class:
\[ \frac{1}{3} \times 70 = \frac{70}{3} \approx 23.33 \]
- For the rest class:
\[ \frac{5}{12} \times 56 = \frac{280}{12} \approx 23.33 \]

4. Now, sum these averages:
\[ \text{Total Average} = 21.25 + 23.33 + 23.33 = 67.91 \]

5. Therefore, the average marks of the whole class is approximately:
\[ \text{Average} \approx 67.91\% \]