The average marks of 30 students are 45 but after checking , there are two mistakes found. After adjustment , if a student got 45 more marks and other student got 15 less marks , then what will be the adjusted average ?

Options

A. 45
B. 44
C. 47
D. 46

Answer

To solve the problem step by step, we will first determine the total marks of the students based on the given average, then adjust for the mistakes, and finally calculate the new average.

### Step 1: Calculate the initial total marks
The average marks of 30 students is given as 45. We can find the total marks by using the formula for average:

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

Rearranging the formula gives us:

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

Substituting the values:

\[ \text{Total Marks} = 45 \times 30 = 1350 \]

### Step 2: Adjust the total marks for the mistakes
We know that one student received 45 more marks and another student received 15 less marks. To find the adjusted total marks, we need to add the increase and subtract the decrease:

\[ \text{Adjusted Total Marks} = \text{Original Total Marks} + \text{Increase} - \text{Decrease} \]

Substituting the values:

\[ \text{Adjusted Total Marks} = 1350 + 45 - 15 \]

Calculating this gives:

\[ \text{Adjusted Total Marks} = 1350 + 45 - 15 = 1350 + 30 = 1380 \]

### Step 3: Calculate the new average
Now, we can find the new average using the adjusted total marks:

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

Substituting the values:

\[ \text{New Average} = \frac{1380}{30} \]

Calculating this gives:

\[ \text{New Average} = 46 \]

### Final Answer
The adjusted average marks of the students is **46**.

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