Quantity I . Profit earned on selling an article as Rs. 450 at `20%` profit
Quantity II. Cost price of the article which is sold at Rs. 84 on `20%` profit

Options

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

Answer

To solve the problem, we will calculate both quantities step by step.

### Step 1: Calculate Quantity I (Q1)
We need to find the cost price (CP) of an article that is sold for Rs. 450 at a profit of 20%.

1. **Understanding Profit Percentage**:
- If the selling price (SP) is Rs. 450 and the profit percentage is 20%, we can express this as:
\[ SP = CP + \text{Profit} \]
- The profit can also be expressed as:
\[ \text{Profit} = \frac{20}{100} \times CP = 0.2 \times CP \]
- Therefore, we can rewrite the selling price equation as:
\[ SP = CP + 0.2 \times CP = 1.2 \times CP \]

2. **Substituting the Selling Price**:
- Substitute SP with 450:
\[ 450 = 1.2 \times CP \]

3. **Solving for Cost Price**:
- To find CP, we divide both sides by 1.2:
\[ CP = \frac{450}{1.2} = 375 \]

4. **Calculating Profit**:
- Now, we can find the profit:
\[ \text{Profit} = SP - CP = 450 - 375 = 75 \]

Thus, Quantity I (Q1) is Rs. 75.

### Step 2: Calculate Quantity II (Q2)
Now we will find the cost price of an article that is sold for Rs. 84 at a profit of 20%.

1. **Understanding the Selling Price**:
- Similar to before, we have:
\[ SP = CP + \text{Profit} \]
- The profit is again:
\[ \text{Profit} = 0.2 \times CP \]
- Thus, we can express the selling price as:
\[ SP = 1.2 \times CP \]

2. **Substituting the Selling Price**:
- Substitute SP with 84:
\[ 84 = 1.2 \times CP \]

3. **Solving for Cost Price**:
- To find CP, we divide both sides by 1.2:
\[ CP = \frac{84}{1.2} = 70 \]

Thus, Quantity II (Q2) is Rs. 70.

### Step 3: Compare Quantities
Now we compare the two quantities:
- Quantity I (Q1) = Rs. 75
- Quantity II (Q2) = Rs. 70

Since 75 > 70, we conclude that Quantity I is greater than Quantity II.

### Final Answer
- **Q1 > Q2**. Therefore, the answer is **Option A**.