Assertion: Equivalent mass of `KMnO_4` is same in the neutral as well as alkaline medium.
Reason: The product formed in both cases in `MnO_2`

Options

A. If both (A) and (R) are correct and (R) is the correct explanation of (A).
B. If both (A) and (R) are correct, but (R) is not the correct explanation of (A).
C. If (A) is correct, but (R) is incorrect.
D. If (A) is incorrect but (R) is correct.

Answer

To solve the assertion and reasoning question regarding the equivalent mass of KMnO4 in neutral and alkaline mediums, we will analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the equivalent mass of KMnO4 is the same in both neutral and alkaline mediums.
- To evaluate this, we need to look at the half-reactions that occur in both mediums and determine the number of electrons transferred.

2. **Half-Reaction in Alkaline Medium**:
- In alkaline medium, the half-reaction for the reduction of permanganate ion (MnO4^-) can be written as:
\[ \text{MnO}_4^- + 2 \text{H}_2\text{O} + 3 \text{e}^- \rightarrow \text{MnO}_2 + 4 \text{OH}^- \]
- Here, 3 electrons are transferred.

3. **Calculating Equivalent Mass in Alkaline Medium**:
- The equivalent mass (E) can be calculated using the formula:
\[ E = \frac{\text{Molar mass}}{\text{Number of electrons transferred}} \]
- The molar mass of KMnO4 is 158 g/mol. Therefore, in alkaline medium:
\[ E = \frac{158}{3} \approx 52.7 \text{ g/equiv} \]

4. **Half-Reaction in Neutral Medium**:
- In neutral medium, the half-reaction is:
\[ \text{MnO}_4^- + 4 \text{H}^+ + 3 \text{e}^- \rightarrow \text{MnO}_2 + 2 \text{H}_2\text{O} \]
- Again, 3 electrons are transferred.

5. **Calculating Equivalent Mass in Neutral Medium**:
- Using the same formula for equivalent mass:
\[ E = \frac{158}{3} \approx 52.7 \text{ g/equiv} \]

6. **Conclusion on Assertion**:
- Since the equivalent mass of KMnO4 is the same in both neutral and alkaline mediums (52.7 g/equiv), the assertion is **true**.

7. **Understanding the Reason**:
- The reason states that the product formed in both cases is MnO2.
- While this statement is also true, it does not explain why the equivalent mass is the same. The equivalent mass depends on the number of electrons transferred, not solely on the product formed.

8. **Conclusion on Reason**:
- The reason is **true**, but it does not correctly explain the assertion.

### Final Answer:
- The assertion is true, and the reason is true but does not provide the correct explanation for the assertion.