A and B are the numerical values of a physical quantity and C and D are its units in two systems of mesurement . If C > D, then

Options

A. `A gt B`
B. A less than B
C. A = B
D. A & B cannot be related

Answer

To solve the problem, we need to analyze the relationship between the numerical values of a physical quantity and its units in two different systems of measurement. Let's break it down step by step:

### Step 1: Understand the relationship between numerical values and units
A physical quantity can be expressed as:
\[ \text{Physical Quantity} = \text{Numerical Value} \times \text{Unit} \]

Let’s denote:
- \( A \) as the numerical value of the physical quantity in the first system,
- \( B \) as the numerical value of the physical quantity in the second system,
- \( C \) as the unit in the first system,
- \( D \) as the unit in the second system.

### Step 2: Establish the relationship between the two systems
From the definition of physical quantities, we can write:
\[ A \times C = B \times D \]

This equation indicates that the physical quantity remains the same regardless of the system of measurement used.

### Step 3: Rearranging the equation
Rearranging the equation gives us:
\[ \frac{A}{B} = \frac{D}{C} \]

### Step 4: Analyze the given condition
We are given that \( C > D \). This implies that:
\[ \frac{D}{C} < 1 \]

### Step 5: Conclude the relationship between A and B
Since \( \frac{A}{B} = \frac{D}{C} \) and \( \frac{D}{C} < 1 \), it follows that:
\[ \frac{A}{B} < 1 \]
This means:
\[ A < B \]

### Final Conclusion
Thus, if \( C > D \), then we conclude that:
\[ A < B \]

### Answer
The correct option is: **A is less than B.**

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