Two leaves A and B are increasing their surface area by 7 `cm^2` in one day. Their initial size was A = 7`cm^2` and B = 70 `cm^2``. Choose correct option w.r.t.their absolute growth and relative growth.

Options

A. Absolute growth rate of A is equal to absolute growth rate of B while relative growth rate of A is less than relative growth of B.
B. Absolute growth rate of A is greater than absolute growth rate of B while relative growth rate of A is equal to relative growth rate of B
C. Absolute growth rate of A is less than absolute growth rate of B while relative growth rate of A is less than relative growth rate of B
D. Absolute growth rate of A is equal to absolute growth rate of B while relative growth rate of A is more than relative growth of B.

Answer

To solve the question regarding the absolute and relative growth of leaves A and B, we will follow these steps:

### Step 1: Identify the initial sizes and growth of the leaves
- Leaf A has an initial size of 7 cm².
- Leaf B has an initial size of 70 cm².
- Both leaves increase their surface area by 7 cm² in one day.

### Step 2: Calculate the absolute growth for both leaves
- The absolute growth is the actual increase in size.
- For both leaves, the absolute growth is:
- Absolute growth of A = 7 cm² (increase)
- Absolute growth of B = 7 cm² (increase)

### Step 3: Calculate the relative growth for both leaves
- Relative growth is calculated using the formula:
\[ \text{Relative Growth} = \left(\frac{\text{Absolute Growth}}{\text{Initial Size}}\right) \times 100 \]
- For leaf A:
\[ \text{Relative Growth of A} = \left(\frac{7}{7}\right) \times 100 = 100\% \]
- For leaf B:
\[ \text{Relative Growth of B} = \left(\frac{7}{70}\right) \times 100 = 10\% \]

### Step 4: Compare absolute and relative growth rates
- **Absolute Growth**:
- Absolute growth of A = 7 cm²
- Absolute growth of B = 7 cm²
- Conclusion: Absolute growth of A = Absolute growth of B

- **Relative Growth**:
- Relative growth of A = 100%
- Relative growth of B = 10%
- Conclusion: Relative growth of A > Relative growth of B

### Step 5: Choose the correct option
Based on the calculations:
- The absolute growth rates of A and B are equal.
- The relative growth rate of A is greater than that of B.

Thus, the correct option is:
- **Option D**: Absolute growth rate of A is equal to absolute growth rate of B while relative growth rate of A is more than relative growth rate of B.

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