In class IX. the average marks of 6 students In science were 48. After the declaration of result, it was observed that the number 45 of a student was misread as 54. The correct average is:

Options

A. 76.5
B. 46.4
C. 46.5
D. 64.9

Answer

To find the correct average marks of the 6 students after correcting the misread marks, we can follow these steps:

### Step 1: Calculate the total marks based on the initial average.
The average marks of the 6 students is given as 48. To find the total marks, we use the formula:

\[ \text{Total Marks} = \text{Average} \times \text{Number of Students} \]

Substituting the values:

\[ \text{Total Marks} = 48 \times 6 = 288 \]

### Step 2: Identify the misread marks and correct them.
It was observed that one student's marks were misread as 54 instead of the actual marks, which were 45. We need to adjust the total marks accordingly.

### Step 3: Adjust the total marks.
To correct the total marks, we need to subtract the misread marks (54) and add the correct marks (45):

\[ \text{Corrected Total Marks} = \text{Total Marks} - \text{Misread Marks} + \text{Correct Marks} \]

Substituting the values:

\[ \text{Corrected Total Marks} = 288 - 54 + 45 = 288 - 9 = 279 \]

### Step 4: Calculate the new average.
Now that we have the corrected total marks, we can find the new average:

\[ \text{New Average} = \frac{\text{Corrected Total Marks}}{\text{Number of Students}} \]

Substituting the values:

\[ \text{New Average} = \frac{279}{6} = 46.5 \]

### Final Answer:
The correct average marks of the 6 students after correcting the misread marks is **46.5**.

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