Directions: In the following question, two quantities I and II are given. Compare both the quantities and choose the correct option and give answer accordingly.
Quantity I: What is the per cent of profit when an article of cost price ₹1250 is sold for ₹1500?
Quantity II: The net discount percentage availed by a customer when he gets two successive discounts of `10%` and `12.5%`

Options

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

Answer

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

### Quantity I: Percentage of Profit

1. **Identify the Cost Price (CP) and Selling Price (SP)**:
- Cost Price (CP) = ₹1250
- Selling Price (SP) = ₹1500

2. **Calculate Profit**:
\[ \text{Profit} = \text{SP} - \text{CP} = 1500 - 1250 = ₹250 \]

3. **Calculate Profit Percentage**:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{250}{1250}\right) \times 100 \]
- Simplify the fraction:
\[ \frac{250}{1250} = \frac{1}{5} = 0.2 \]
- Now multiply by 100:
\[ 0.2 \times 100 = 20\% \]

### Quantity II: Net Discount Percentage

1. **Identify the Successive Discounts**:
- First Discount = 10%
- Second Discount = 12.5%

2. **Assume an Initial Price**:
- Let the initial price be ₹100.

3. **Calculate Price After First Discount**:
\[ \text{Price after 10% discount} = 100 - (10\% \text{ of } 100) = 100 - 10 = ₹90 \]

4. **Calculate Price After Second Discount**:
\[ \text{Price after 12.5% discount on ₹90} = 90 - (12.5\% \text{ of } 90) = 90 - 11.25 = ₹78.75 \]

5. **Calculate Net Discount**:
\[ \text{Net Discount} = \text{Initial Price} - \text{Final Price} = 100 - 78.75 = ₹21.25 \]

6. **Calculate Net Discount Percentage**:
\[ \text{Net Discount Percentage} = \left(\frac{\text{Net Discount}}{\text{Initial Price}}\right) \times 100 = \left(\frac{21.25}{100}\right) \times 100 = 21.25\% \]

### Final Comparison

- **Quantity I**: 20%
- **Quantity II**: 21.25%

Since 20% (Quantity I) is less than 21.25% (Quantity II), we conclude that:

**Quantity I < Quantity II**

### Answer:
The correct option is that Quantity I is smaller than Quantity II.

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