Direction: In the given question, read the given statement and compare the two given quantities on its basis.
There are three positive number a, b and c. The average of a and b is less than the average of b and c by 1.
Quantity I. Value of c
Quantity II. Value of a

Options

A. Quantity I = Quantity II
B. Quantity I `gt` Quantity II
C. Quantity I `lt` Quantity II
D. Quantity I `ge` Quantity II

Answer

To solve the problem step by step, we will analyze the given statement and derive the necessary equations to compare the two quantities.

### Step 1: Understand the given information
We have three positive numbers: \( a \), \( b \), and \( c \). The problem states that the average of \( a \) and \( b \) is less than the average of \( b \) and \( c \) by 1.

### Step 2: Write the expressions for the averages
The average of \( a \) and \( b \) can be expressed as:
\[ \text{Average of } a \text{ and } b = \frac{a + b}{2} \]
The average of \( b \) and \( c \) can be expressed as:
\[ \text{Average of } b \text{ and } c = \frac{b + c}{2} \]

### Step 3: Set up the inequality based on the problem statement
According to the problem, the average of \( a \) and \( b \) is less than the average of \( b \) and \( c \) by 1. This can be written as:
\[ \frac{a + b}{2} + 1 = \frac{b + c}{2} \]

### Step 4: Clear the fractions by multiplying through by 2
To eliminate the fractions, we multiply the entire equation by 2:
\[ a + b + 2 = b + c \]

### Step 5: Rearrange the equation
Now, we can rearrange the equation to isolate \( c \):
\[ a + b + 2 - b = c \]
This simplifies to:
\[ c = a + 2 \]

### Step 6: Compare the values of \( c \) and \( a \)
From the equation \( c = a + 2 \), we can see that \( c \) is equal to \( a \) plus 2. Since \( a \) is a positive number, it follows that:
\[ c > a \]

### Conclusion
Given that \( c \) is greater than \( a \), we can conclude that:
- **Quantity I (Value of c)** is greater than **Quantity II (Value of a)**.

Thus, the answer is:
**Quantity I is greater than Quantity II.**