The marks of Nine students in ascending order of a test are given below with Median as 34, the value of k is:
12, 16, k, 28, k + 5, 32, 47, 53, 57

Options

A. 27
B. 30
C. 29
D. 32

Answer

To find the value of \( k \) in the given set of marks, we need to follow these steps:

### Step 1: Understand the Median
The median of a set of numbers is the middle value when the numbers are arranged in ascending order. Since there are 9 students, the median will be the 5th value in the ordered list.

### Step 2: Set Up the Ordered List
The marks of the nine students are given as:
\[ 12, 16, k, 28, k + 5, 32, 47, 53, 57 \]

### Step 3: Identify the Position of the Median
Since there are 9 numbers, the median will be the 5th number in the ordered list. According to the problem, the median is given as 34.

### Step 4: Set Up the Equation
From the ordered list, the 5th number is \( k + 5 \). Therefore, we can set up the equation:
\[ k + 5 = 34 \]

### Step 5: Solve for \( k \)
To find \( k \), we subtract 5 from both sides of the equation:
\[ k = 34 - 5 \]
\[ k = 29 \]

### Step 6: Verify the Solution
Now, let's check if \( k = 29 \) fits into the list and maintains the order:
- If \( k = 29 \), then \( k + 5 = 34 \).
- The ordered list becomes: \( 12, 16, 29, 28, 34, 32, 47, 53, 57 \).
- Rearranging gives us: \( 12, 16, 28, 29, 34, 32, 47, 53, 57 \).

The 5th number is indeed 34, confirming that our solution is correct.

### Final Answer
Thus, the value of \( k \) is:
\[ \boxed{29} \]