Average marks obtained by 9 students in one row of a class is 45. One student with 35 marks exchanges his seat with a student securing 48 marks. What is the average marks of these 9 students of this row?

Options

A. 56.4
B. 46.4
C. 47.6
D. 45.6

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the total marks of the 9 students initially.
The average marks obtained by the 9 students is given as 45.

To find the total marks (let's call it \( T \)), we use the formula for average:

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

So,

\[ T = \text{Average} \times \text{Number of Students} = 45 \times 9 = 405 \]

### Step 2: Determine the new total marks after the exchange.
One student with 35 marks exchanges his seat with another student who has 48 marks.

To find the new total marks, we will subtract the marks of the student leaving (35) and add the marks of the student coming in (48):

\[ \text{New Total Marks} = T - 35 + 48 = 405 - 35 + 48 \]

Calculating this gives:

\[ 405 - 35 = 370 \]
\[ 370 + 48 = 418 \]

So, the new total marks is 418.

### Step 3: Calculate the new average marks.
Now, we can calculate the new average using the new total marks:

\[ \text{New Average} = \frac{\text{New Total Marks}}{\text{Number of Students}} = \frac{418}{9} \]

Calculating this gives:

\[ \frac{418}{9} \approx 46.4444 \]

Rounding this to one decimal place gives us:

\[ \text{New Average} \approx 46.4 \]

### Final Answer:
The new average marks of the 9 students after the exchange is **46.4**.

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