Quantity I : Marked price of article, if article is marked at `50%` above cost price and on selling the article profit earned is ` 20%` and S.P is Rs. 1020
Quantity II : Total cost of fencing a square of side 37.5 meter and cost of wire is Rs. 0.17 per centimeter

Options

A. A)Quantity I ` gt` Quantity II
B. B)Quantity I ` lt` Quantity II
C. C)Quantity I ` ge` Quantity II
D. D)Quantity I = Quantity II or no relation

Answer

To solve the problem, we will break it down into two parts: Quantity I and Quantity II.

### Quantity I: Marked Price of the Article

1. **Assume Cost Price (CP)**:
Let's assume the cost price of the article is \( CP = 100 \) (this is an arbitrary choice to simplify calculations).

2. **Calculate Selling Price (SP)**:
The profit earned is 20%. Therefore, the selling price can be calculated as:
\[ SP = CP + (20\% \text{ of } CP) = 100 + 0.2 \times 100 = 100 + 20 = 120 \]

3. **Relate Selling Price to Given Value**:
We know from the problem that the selling price is Rs. 1020. Therefore, we can set up the equation:
\[ 120 \text{ (units)} = 1020 \text{ (Rs)} \]

4. **Find the Value of One Unit**:
To find the value of one unit, we divide:
\[ 1 \text{ unit} = \frac{1020}{120} = 8.5 \text{ Rs} \]

5. **Calculate Marked Price (MP)**:
The marked price is 50% above the cost price. Therefore, we calculate:
\[ MP = CP + (50\% \text{ of } CP) = 100 + 0.5 \times 100 = 100 + 50 = 150 \]

6. **Convert Marked Price to Rs**:
Now, we need to convert this into Rs using the value of one unit:
\[ MP = 150 \text{ (units)} \times 8.5 \text{ (Rs/unit)} = 1275 \text{ Rs} \]

### Quantity II: Total Cost of Fencing a Square

1. **Calculate the Perimeter of the Square**:
The side of the square is given as 37.5 meters. The perimeter (P) of a square is given by:
\[ P = 4 \times \text{side} = 4 \times 37.5 = 150 \text{ meters} \]

2. **Convert Perimeter to Centimeters**:
Since the cost of wire is given in Rs per centimeter, we convert the perimeter from meters to centimeters:
\[ 150 \text{ meters} = 150 \times 100 = 15000 \text{ centimeters} \]

3. **Calculate the Total Cost of Fencing**:
The cost of wire is Rs. 0.17 per centimeter. Therefore, the total cost (C) can be calculated as:
\[ C = \text{Perimeter} \times \text{Cost per centimeter} = 15000 \times 0.17 = 2550 \text{ Rs} \]

### Final Comparison of Quantities

- Quantity I (Marked Price) = Rs. 1275
- Quantity II (Cost of Fencing) = Rs. 2550

### Conclusion:
Comparing the two quantities:
- Quantity I < Quantity II

Thus, the answer is that Quantity I is less than Quantity II.