A : Out of the measurements A = 20.00 and B = 20.000, B is more accurate.
R : Percentage error in B is less than the percentage error in A.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4).

Answer

To solve the question, we need to analyze the accuracy of the two measurements A and B based on their least counts and the concept of percentage error.

### Step 1: Identify the Measurements
- Measurement A = 20.00
- Measurement B = 20.000

### Step 2: Determine the Least Counts
- The least count of measurement A (20.00) is 0.01 (the last digit is in the hundredths place).
- The least count of measurement B (20.000) is 0.001 (the last digit is in the thousandths place).

### Step 3: Understand the Concept of Accuracy
- Accuracy is determined by the least count of the measuring instrument. A smaller least count indicates a more precise measurement.
- Therefore, since the least count of B (0.001) is less than that of A (0.01), measurement B is more accurate than measurement A.

### Step 4: Calculate the Percentage Error
- The formula for percentage error is given by:
\[ \text{Percentage Error} = \left(\frac{\text{Least Count}}{\text{Measured Value}}\right) \times 100 \]

#### For Measurement A:
\[ \text{Percentage Error in A} = \left(\frac{0.01}{20.00}\right) \times 100 = 0.05\% \]

#### For Measurement B:
\[ \text{Percentage Error in B} = \left(\frac{0.001}{20.000}\right) \times 100 = 0.005\% \]

### Step 5: Compare the Percentage Errors
- Percentage Error in A = 0.05%
- Percentage Error in B = 0.005%

Since 0.005% (B) is less than 0.05% (A), this confirms that the percentage error in B is indeed less than that in A.

### Conclusion
- Assertion (A): B is more accurate than A. **True**
- Reason (R): The percentage error in B is less than the percentage error in A. **True**

Both the assertion and reason are correct, and the reason correctly explains the assertion.

### Final Answer
Both A and R are true, and R explains A.

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