The average of marks in English for ten students was found to be 45. Later on, it was discovered that in case of one student, the marks 46 were misread as 64. The correct average is

Options

A. (a) 43.2
B. (b) 45.5
C. (c) 49.3
D. (d) 53.2

Answer

To find the correct average of marks in English for the ten students after correcting the misread marks, we can follow these steps:

### Step 1: Calculate the total recorded marks based on the initial average.
The average marks for ten students is given as 45. To find the total recorded marks, we multiply the average by the number of students.

\[ \text{Total recorded marks} = \text{Average} \times \text{Number of students} = 45 \times 10 = 450 \]

### Step 2: Identify the incorrect and correct marks for the student.
It is stated that one student's marks were misread. The marks were recorded as 64 instead of the correct marks of 46.

### Step 3: Adjust the total recorded marks to reflect the correct marks.
To correct the total recorded marks, we need to subtract the incorrect marks (64) and add the correct marks (46).

\[ \text{Corrected total marks} = \text{Total recorded marks} - \text{Incorrect marks} + \text{Correct marks} \]
\[ \text{Corrected total marks} = 450 - 64 + 46 \]
\[ \text{Corrected total marks} = 450 - 64 + 46 = 450 - 18 = 432 \]

### Step 4: Calculate the new average.
Now that we have the corrected total marks, we can find the new average by dividing the corrected total marks by the number of students.

\[ \text{New average} = \frac{\text{Corrected total marks}}{\text{Number of students}} = \frac{432}{10} = 43.2 \]

### Final Answer:
The correct average of marks in English for the ten students is **43.2**.

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