The average of 20, 25, 35, 15, a, 30 is 22.5. The value of a is :

Options

A. 13
B. 12.5
C. 10
D. 15

Answer

To find the value of \( a \) in the given problem, we need to follow these steps:

### Step 1: Write down the formula for average
The average of a set of numbers is calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of all numbers}}{\text{Total count of numbers}} \]
In this case, we have 6 numbers: 20, 25, 35, 15, \( a \), and 30.

### Step 2: Set up the equation
According to the problem, the average of these numbers is given as 22.5. Therefore, we can set up the equation:
\[ \frac{20 + 25 + 35 + 15 + a + 30}{6} = 22.5 \]

### Step 3: Calculate the sum of the known numbers
Now, let's calculate the sum of the known numbers:
\[ 20 + 25 + 35 + 15 + 30 = 125 \]
So, we can rewrite our equation as:
\[ \frac{125 + a}{6} = 22.5 \]

### Step 4: Eliminate the fraction by multiplying both sides by 6
To eliminate the fraction, multiply both sides of the equation by 6:
\[ 125 + a = 22.5 \times 6 \]

### Step 5: Calculate \( 22.5 \times 6 \)
Now, calculate \( 22.5 \times 6 \):
\[ 22.5 \times 6 = 135 \]
So, we have:
\[ 125 + a = 135 \]

### Step 6: Solve for \( a \)
Now, subtract 125 from both sides to find \( a \):
\[ a = 135 - 125 \]
\[ a = 10 \]

### Conclusion
The value of \( a \) is \( 10 \).

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