Study the following statements carefully and select the correct option.
Statement-1 : If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.
Statement-il : Curved surface area is increased when diameter decreases.

Options

A. Both Statement-l and Statement-II are true.
B. Statement-l is true but Statement-II is false.
C. Statement-l is false but Statement-II is true.
D. Both Statement-l and Statement- II are false.

Explanation

To solve the problem, we need to analyze the two statements provided and determine their validity based on the properties of a sphere and the formulas related to its surface area.

### Step-by-Step Solution:

1. **Understanding the Curved Surface Area (CSA) of a Sphere**:
The formula for the curved surface area (CSA) of a sphere is given by:
\[ \text{CSA} = 4\pi r^2 \]
where \( r \) is the radius of the sphere. Since the diameter \( D \) is twice the radius, we have:
\[ r = \frac{D}{2} \]
Thus, we can express CSA in terms of diameter:
\[ \text{CSA} = 4\pi \left(\frac{D}{2}\right)^2 = \pi D^2 \]

2. **Calculating the New Diameter After a 25% Decrease**:
If the diameter is decreased by 25%, the new diameter \( D' \) can be calculated as:
\[ D' = D - 0.25D = 0.75D \]

3. **Calculating the New Curved Surface Area**:
Now, we calculate the new CSA using the new diameter \( D' \):
\[ \text{CSA}' = \pi (D')^2 = \pi (0.75D)^2 = \pi \left(\frac{9}{16}D^2\right) = \frac{9\pi D^2}{16} \]

4. **Finding the Percentage Decrease in CSA**:
The original CSA is \( \pi D^2 \). The decrease in CSA can be calculated as:
\[ \text{Decrease} = \text{Original CSA} - \text{New CSA} = \pi D^2 - \frac{9\pi D^2}{16} = \pi D^2 \left(1 - \frac{9}{16}\right) = \pi D^2 \left(\frac{7}{16}\right) \]
The percentage decrease is given by:
\[ \text{Percentage Decrease} = \frac{\text{Decrease}}{\text{Original CSA}} \times 100 = \frac{\frac{7\pi D^2}{16}}{\pi D^2} \times 100 = \frac{7}{16} \times 100 = 43.75\% \]

5. **Evaluating Statement 1**:
Statement 1 claims that if the diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%. From our calculations, this statement is **true**.

6. **Evaluating Statement 2**:
Statement 2 claims that the curved surface area increases when the diameter decreases. However, from the formula \( \text{CSA} = \pi D^2 \), we see that CSA is directly proportional to the square of the diameter. Therefore, if the diameter decreases, the CSA must also decrease. Thus, this statement is **false**.

### Conclusion:
- **Statement 1**: True
- **Statement 2**: False

The correct option is that Statement 1 is true and Statement 2 is false.