Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements sufficient to answer the question. Read both the statements and give answer:
There are two cylindrical rollers-bigger and smaller. How many rotations will the bigger roller take to flatten a strech of land (X)?
The respective ratio of the radii of the bigger and the smaller rollers is 7:3. Both the rollers are of the same length.
II. The smaller roller takes 63 rotations to flatten the stretch of land (X).

Options

A. if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
B. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
C. if the data in statement I alone or in statement II alone are sufficient to answer the question.
D. if the data in both the statements I and II together are sufficient to answer the question.

Answer

To solve the problem, we need to determine how many rotations the bigger roller will take to flatten a stretch of land (X) based on the information provided in the two statements.

### Step-by-Step Solution:

1. **Understand the Problem**: We have two cylindrical rollers, one bigger and one smaller. We need to find out how many rotations the bigger roller takes to flatten a stretch of land (X).

2. **Analyze Statement I**:
- The ratio of the radii of the bigger roller to the smaller roller is given as 7:3.
- Let the radius of the bigger roller be \(7x\) and the radius of the smaller roller be \(3x\).
- Both rollers have the same length (height), which we can denote as \(A\).
- This statement alone does not provide enough information to determine the number of rotations the bigger roller will take.

**Hint**: Ratios give us relative sizes but not absolute values or the number of rotations.

3. **Analyze Statement II**:
- The smaller roller takes 63 rotations to flatten the stretch of land (X).
- This means that the area flattened by the smaller roller in 63 rotations is equal to the area of land (X).
- However, without knowing the area that the bigger roller can flatten in one rotation, we cannot determine how many rotations it will take for the bigger roller.

**Hint**: Knowing the number of rotations for one roller does not help us find the rotations for another without a relationship between their areas.

4. **Combine Both Statements**:
- The area flattened by the smaller roller in one rotation is given by the formula for the lateral surface area of a cylinder:
\[ \text{Area}_{\text{smaller}} = 2\pi(3x)A \]
- Thus, the total area flattened by the smaller roller in 63 rotations is:
\[ \text{Total Area} = 63 \times 2\pi(3x)A \]
- The area flattened by the bigger roller in one rotation is:
\[ \text{Area}_{\text{bigger}} = 2\pi(7x)A \]
- To find the number of rotations \(R\) the bigger roller takes, we can set up the equation:
\[ R = \frac{\text{Total Area}}{\text{Area}_{\text{bigger}}} \]
- Substituting the areas:
\[ R = \frac{63 \times 2\pi(3x)A}{2\pi(7x)A} \]
- Simplifying gives:
\[ R = \frac{63 \times 3}{7} = 27 \]

5. **Conclusion**:
- The bigger roller will take 27 rotations to flatten the stretch of land (X).

### Final Answer:
The data in both statements together is sufficient to answer the question.