Two classes M and n have average marks 25 and 40 respectively, the overall average obtained is 30. The ratio of the students in the class M and N is

Options

A. `2:1`
B. `5:6`
C. `5:3`
D. `1:2`

Answer

To solve the problem, we need to find the ratio of the number of students in classes M and N based on their average marks. Let's break it down step by step.

### Step-by-Step Solution:

1. **Identify Given Information:**
- Average marks of class M = 25
- Average marks of class N = 40
- Overall average marks = 30

2. **Let the Number of Students:**
- Let the number of students in class M be \( m \).
- Let the number of students in class N be \( n \).

3. **Calculate Total Marks:**
- Total marks of class M = Average marks of M × Number of students in M = \( 25m \)
- Total marks of class N = Average marks of N × Number of students in N = \( 40n \)

4. **Calculate Overall Total Marks:**
- Total marks of both classes = Average marks × Total number of students = \( 30(m + n) \)

5. **Set Up the Equation:**
- According to the problem, the total marks from both classes should equal the overall total marks:
\[ 25m + 40n = 30(m + n) \]

6. **Expand and Rearrange the Equation:**
- Expanding the right side:
\[ 25m + 40n = 30m + 30n \]
- Rearranging gives:
\[ 25m + 40n - 30m - 30n = 0 \]
- Simplifying further:
\[ -5m + 10n = 0 \]
- This can be rewritten as:
\[ 5m = 10n \]

7. **Find the Ratio:**
- Dividing both sides by 5:
\[ m = 2n \]
- Therefore, the ratio of students in class M to students in class N is:
\[ \frac{m}{n} = \frac{2n}{n} = 2:1 \]

### Conclusion:
The ratio of the number of students in class M to the number of students in class N is \( 2:1 \).