If mean of 5,10,15,P,20,35,40 is 21. Then the value of P will be

Options

A. 18
B. 22
C. 25
D. 30

Answer

To find the value of \( P \) in the given set of numbers \( 5, 10, 15, P, 20, 35, 40 \) with a mean of \( 21 \), we can follow these steps:

### Step 1: Understand the formula for mean
The mean (average) of a set of numbers is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]

### Step 2: Identify the total number of observations
In this case, the total number of observations is \( 7 \) (the numbers are \( 5, 10, 15, P, 20, 35, 40 \)).

### Step 3: Set up the equation for the mean
According to the problem, the mean of the numbers is given as \( 21 \). Therefore, we can set up the equation:
\[ 21 = \frac{5 + 10 + 15 + P + 20 + 35 + 40}{7} \]

### Step 4: Calculate the sum of known numbers
Now, let's calculate the sum of the known numbers:
\[ 5 + 10 + 15 + 20 + 35 + 40 = 125 \]
So, we can rewrite the equation as:
\[ 21 = \frac{125 + P}{7} \]

### Step 5: Multiply both sides by 7
To eliminate the fraction, multiply both sides of the equation by \( 7 \):
\[ 21 \times 7 = 125 + P \]
Calculating the left side:
\[ 147 = 125 + P \]

### Step 6: Solve for \( P \)
Now, isolate \( P \) by subtracting \( 125 \) from both sides:
\[ P = 147 - 125 \]
Calculating the right side:
\[ P = 22 \]

### Conclusion
The value of \( P \) is \( 22 \).

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