Directions : In each of the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer as
Assertion : Estimated sum of 8001 and 457 is 8500.
Reason : Estimation is done by rounding off the numbers to the nearest places.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the question step by step, let's analyze the assertion and the reason given:

**Assertion:** The estimated sum of 8001 and 457 is 8500.

**Reason:** Estimation is done by rounding off the numbers to the nearest places.

### Step 1: Round off the numbers
- First, we need to round off both numbers to the nearest hundred.
- For **8001**, when rounding to the nearest hundred, we look at the last two digits (01). Since 01 is less than 50, we round down to **8000**.
- For **457**, we look at the last two digits (57). Since 57 is greater than 50, we round up to **500**.

### Step 2: Calculate the estimated sum
- Now, we add the rounded numbers:
- 8000 (rounded value of 8001) + 500 (rounded value of 457) = **8500**.

### Step 3: Verify the assertion
- The assertion states that the estimated sum of 8001 and 457 is 8500. Our calculation confirms that the estimated sum is indeed **8500**.

### Step 4: Analyze the reason
- The reason states that estimation is done by rounding off the numbers to the nearest places. This is true as we have rounded both numbers to the nearest hundred to find the estimated sum.

### Conclusion
- Both the assertion and the reason are correct. The reason provides a valid explanation for the assertion.

### Final Answer
- Therefore, the correct answer is that both the assertion and the reason are true, and the reason is the correct explanation of the assertion.