When all teachers in a school are made in rows of 64, 34 such rows are formed. If the teachers are made to stand in the rows of 32, how many such rows can be formed ?

Options

A. 38
B. 58
C. 48
D. 68

Answer

To solve the problem, we need to find out how many rows can be formed when the teachers are arranged in rows of 32, given that when they are arranged in rows of 64, there are 34 rows.

### Step-by-Step Solution:

1. **Calculate the Total Number of Teachers:**
- When the teachers are arranged in rows of 64 and there are 34 rows, the total number of teachers can be calculated as:
\[ \text{Total Teachers} = \text{Number of Rows} \times \text{Number of Teachers per Row} = 34 \times 64 \]

2. **Perform the Multiplication:**
- Now, calculate \(34 \times 64\):
\[ 34 \times 64 = 2176 \]
- So, the total number of teachers is 2176.

3. **Rearranging Teachers in Rows of 32:**
- Now, we need to find out how many rows can be formed if the teachers are arranged in rows of 32. We can use the total number of teachers calculated in the previous step:
\[ \text{Number of Rows} = \frac{\text{Total Teachers}}{\text{Number of Teachers per Row}} = \frac{2176}{32} \]

4. **Perform the Division:**
- Now, calculate \(2176 \div 32\):
\[ 2176 \div 32 = 68 \]
- Therefore, when the teachers are arranged in rows of 32, 68 rows can be formed.

### Final Answer:
The number of rows that can be formed when the teachers are arranged in rows of 32 is **68**.

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