The mean weight of 9 items is 15. If one more item is added to the series the mean becomes 16. The value of 10th item is (a) `35` (b) `30` (c) `25` (d) `20`

Options

A. 35
B. 30
C. 25
D. 20

Answer

To solve the problem step by step, we will follow the information given in the question and apply the formula for the mean.

### Step 1: Understand the given information
We know that the mean weight of 9 items is 15.

### Step 2: Calculate the sum of the first 9 items
The formula for the mean is:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]
From the problem, we have:
\[ 15 = \frac{\text{Sum of 9 items}}{9} \]
To find the sum of the 9 items, we rearrange the formula:
\[ \text{Sum of 9 items} = 15 \times 9 = 135 \]

### Step 3: Introduce the 10th item
Let the weight of the 10th item be \( x \). Now, we have a total of 10 items.

### Step 4: Calculate the new mean with the 10th item
The mean of the 10 items is given as 16. We can set up the equation using the mean formula again:
\[ 16 = \frac{135 + x}{10} \]
To eliminate the fraction, we multiply both sides by 10:
\[ 160 = 135 + x \]

### Step 5: Solve for \( x \)
Now, we isolate \( x \):
\[ x = 160 - 135 \]
\[ x = 25 \]

### Conclusion
The value of the 10th item is \( 25 \).

### Final Answer
The value of the 10th item is (c) `25`.

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