In these question two equations numebred I and numberd II are given. You have to solve both the equations and find out the correct option.
Quantity I: An ore contains `24%`, `40%` and `36%` of Copper, Zinc and Tin respectively. Then how many kg of ore is required to extract 260 kg of Zinc?
Quantity II: What is the difference between compound interest and simple interest for an amount of 15000 at the rate of `8%` for two years?

Options

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

Answer

To solve the problem, we need to address both Quantity I and Quantity II separately.

### Quantity I:
An ore contains `24%`, `40%`, and `36%` of Copper, Zinc, and Tin respectively. We need to find out how many kg of ore is required to extract `260 kg` of Zinc.

1. **Understanding the Composition**:
The ore contains `40%` Zinc. This means that in `100 kg` of ore, there are `40 kg` of Zinc.

2. **Setting Up the Equation**:
Let the total weight of the ore be `x kg`. Since `40%` of the ore is Zinc, we can express the amount of Zinc in terms of `x`:
\[ \text{Zinc in } x \text{ kg of ore} = 0.40 \times x \]

3. **Setting Up the Equation for Zinc**:
We want this amount to equal `260 kg`:
\[ 0.40x = 260 \]

4. **Solving for x**:
To find `x`, we can rearrange the equation:
\[ x = \frac{260}{0.40} \]
\[ x = \frac{260 \times 100}{40} = \frac{26000}{40} = 650 \text{ kg} \]

### Quantity II:
We need to find the difference between compound interest and simple interest for an amount of `15000` at the rate of `8%` for `2 years`.

1. **Calculating Simple Interest (SI)**:
The formula for Simple Interest is:
\[ \text{SI} = P \times r \times t \]
Where:
- \( P = 15000 \)
- \( r = \frac{8}{100} = 0.08 \)
- \( t = 2 \)

Plugging in the values:
\[ \text{SI} = 15000 \times 0.08 \times 2 = 2400 \]

2. **Calculating Compound Interest (CI)**:
The formula for Compound Interest is:
\[ \text{CI} = P \left(1 + r\right)^t - P \]
Plugging in the values:
\[ \text{CI} = 15000 \left(1 + 0.08\right)^2 - 15000 \]
\[ = 15000 \left(1.08\right)^2 - 15000 \]
\[ = 15000 \times 1.1664 - 15000 \]
\[ = 17496 - 15000 = 2496 \]

3. **Finding the Difference**:
Now, we find the difference between CI and SI:
\[ \text{Difference} = \text{CI} - \text{SI} = 2496 - 2400 = 96 \]

### Conclusion:
- Quantity I: 650 kg of ore is required to extract 260 kg of Zinc.
- Quantity II: The difference between compound interest and simple interest is 96.

### Final Comparison:
Since `650 kg` (Quantity I) is greater than `96` (Quantity II), we conclude that Quantity I is greater than Quantity II.