Choose the correct statements from the following by considering two leaves A and B whose initial sizes are `5 cm^2` and `50 cm^2` respectively and after a period of time their sizes are `10 cm^2` and `55 cm^2` respectively
(A) Their absolute growth rates are equal. (B) The absolute growth rate of A is more. (C) The relative growth rate of A is more. (D) The relative growth rate of B is more.

Options

A. A and C
B. B and C
C. A and D
D. D and C

Answer

To solve the problem, we need to calculate the absolute and relative growth rates of leaves A and B based on the given sizes.

### Step-by-Step Solution:

1. **Identify Initial and Final Sizes**:
- Leaf A: Initial size = 5 cm², Final size = 10 cm²
- Leaf B: Initial size = 50 cm², Final size = 55 cm²

2. **Calculate Absolute Growth Rates**:
- Absolute growth is calculated as:
\[ \text{Absolute Growth} = \text{Final Size} - \text{Initial Size} \]
- For Leaf A:
\[ \text{Absolute Growth of A} = 10 \, \text{cm}^2 - 5 \, \text{cm}^2 = 5 \, \text{cm}^2 \]
- For Leaf B:
\[ \text{Absolute Growth of B} = 55 \, \text{cm}^2 - 50 \, \text{cm}^2 = 5 \, \text{cm}^2 \]

3. **Compare Absolute Growth Rates**:
- Both leaves A and B have an absolute growth of 5 cm². Thus, their absolute growth rates are equal.

4. **Calculate Relative Growth Rates**:
- Relative growth is calculated as:
\[ \text{Relative Growth} = \frac{\text{Final Size} - \text{Initial Size}}{\text{Initial Size}} \]
- For Leaf A:
\[ \text{Relative Growth of A} = \frac{10 \, \text{cm}^2 - 5 \, \text{cm}^2}{5 \, \text{cm}^2} = \frac{5 \, \text{cm}^2}{5 \, \text{cm}^2} = 1 \]
- For Leaf B:
\[ \text{Relative Growth of B} = \frac{55 \, \text{cm}^2 - 50 \, \text{cm}^2}{50 \, \text{cm}^2} = \frac{5 \, \text{cm}^2}{50 \, \text{cm}^2} = 0.1 \]

5. **Compare Relative Growth Rates**:
- The relative growth rate of A (1) is greater than that of B (0.1).

6. **Evaluate the Statements**:
- (A) Their absolute growth rates are equal. **(True)**
- (B) The absolute growth rate of A is more. **(False)**
- (C) The relative growth rate of A is more. **(True)**
- (D) The relative growth rate of B is more. **(False)**

### Final Conclusion:
The correct statements are (A) and (C).