A child subtracted two numbers as shown below
``{:(83),(-27),(underlineoverline(64)):}`
which one of the following statements gives idea about the child's learning of subtraction ?

Options

A. It is a mistake and it can be rectified by repeated practice
B. the child has misconceptions about place value in the process of subtraction
C. the child does not know how to subtract
D. the child knows the process of subtraction of two-digit numbers

Explanation

To solve the problem, we need to analyze the child's subtraction process and determine which statement best describes their understanding of subtraction.

### Step-by-Step Solution:

1. **Identify the Numbers**: The child subtracted 27 from 83. We can express this as:
\[ 83 - 27 \]

2. **Perform the Subtraction**: The child wrote the result as 64. Let's break down the subtraction:
- The child attempted to subtract the units (3 from 7).
- Since 3 is less than 7, the child incorrectly wrote:
\[ 3 - 7 = 4 \]
- Then, the child subtracted the tens (8 from 2) and wrote:
\[ 8 - 2 = 6 \]
- Combining these results, the child wrote:
\[ 64 \]

3. **Recognize the Error**: The correct process for subtracting 27 from 83 should involve borrowing:
- The child should have borrowed 1 from the tens place (making the 8 a 7) and added 10 to the 3 in the units place (making it 13).
- Therefore, the correct subtraction should be:
\[ 13 - 7 = 6 \quad \text{(after borrowing)} \]
\[ 7 - 2 = 5 \]
- Thus, the correct answer should be:
\[ 83 - 27 = 56 \]

4. **Determine the Learning Issue**: The child’s mistake indicates a misunderstanding of the borrowing process in subtraction, particularly related to place values.

5. **Choose the Correct Statement**: Given the analysis, the statement that best describes the child's learning of subtraction is:
- **Option B**: The child has misconceptions about place value in the process of subtraction.

### Final Answer:
The correct statement is **Option B**: The child has misconceptions about place value in the process of subtraction.