If the difference between the average of x, y and y, z is 12, then the difference between x and z is :

Options

A. 24
B. 48
C. 12
D. 6

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript:

### Step 1: Understand the problem
We are given that the difference between the average of \(x\) and \(y\) and the average of \(y\) and \(z\) is 12.

### Step 2: Write down the averages
The average of \(x\) and \(y\) is given by:
\[ \text{Average of } x \text{ and } y = \frac{x + y}{2} \]
The average of \(y\) and \(z\) is given by:
\[ \text{Average of } y \text{ and } z = \frac{y + z}{2} \]

### Step 3: Set up the equation
According to the problem, the difference between these two averages is 12:
\[ \frac{x + y}{2} - \frac{y + z}{2} = 12 \]

### Step 4: Simplify the equation
We can simplify the left side of the equation:
\[ \frac{x + y - (y + z)}{2} = 12 \]
This simplifies to:
\[ \frac{x - z}{2} = 12 \]

### Step 5: Multiply both sides by 2
To eliminate the fraction, we multiply both sides by 2:
\[ x - z = 24 \]

### Step 6: Find the difference between \(x\) and \(z\)
The equation \(x - z = 24\) shows that the difference between \(x\) and \(z\) is 24.

### Conclusion
Thus, the difference between \(x\) and \(z\) is:
\[ \boxed{24} \]

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