The average marks in Science subject of a class of 20 students is 68. If the marks of two students were misread are 48 and 65 of the actual marks 72 and 61 respectively, then what would be the correct average ?

Options

A. `68.5`
B. 69
C. `69.5`
D. 70

Answer

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

### Step 1: Calculate the total marks based on the average
The average marks of the class is given as 68 for 20 students. We can calculate the total marks using the formula:

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

\[ \text{Total Marks} = 68 \times 20 = 1360 \]

### Step 2: Identify the misread marks and the actual marks
The misread marks of the two students are 48 and 65. The actual marks for these students are 72 and 61, respectively.

### Step 3: Calculate the difference between actual and misread marks
Now, we calculate the total difference in marks due to the misreading:

\[ \text{Difference for Student 1} = 72 - 48 = 24 \]
\[ \text{Difference for Student 2} = 61 - 65 = -4 \]

### Step 4: Calculate the total difference
Now, we can find the total difference in marks:

\[ \text{Total Difference} = 24 + (-4) = 20 \]

### Step 5: Adjust the total marks
To find the correct total marks, we add the total difference to the previously calculated total marks:

\[ \text{Correct Total Marks} = 1360 + 20 = 1380 \]

### Step 6: Calculate the correct average
Now, we can find the correct average by dividing the correct total marks by the number of students:

\[ \text{Correct Average} = \frac{\text{Correct Total Marks}}{\text{Number of Students}} = \frac{1380}{20} = 69 \]

### Final Answer
The correct average marks after adjusting for the misread marks is **69**.

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