If the average weight of the class of students is 15 and the average weight of another class of students is 30, then the find the ratio of the students of the first class to the another class of 30 students when the average weight of both the classes is 25:

Options

A. 1:2
B. 2:1
C. 1:3
D. 3:4

Answer

To solve the problem of finding the ratio of the number of students in the first class (with an average weight of 15) to the number of students in the second class (with an average weight of 30), given that the combined average weight of both classes is 25, we can use the method of alligation.

### Step-by-Step Solution:

1. **Identify the Average Weights:**
- Average weight of the first class (A1) = 15
- Average weight of the second class (A2) = 30
- Combined average weight (A) = 25

2. **Calculate the Differences:**
- Difference between the average weight of the second class and the combined average:
\[ A2 - A = 30 - 25 = 5 \]
- Difference between the combined average and the average weight of the first class:
\[ A - A1 = 25 - 15 = 10 \]

3. **Set Up the Ratio:**
- The ratio of the number of students in the first class (N1) to the number of students in the second class (N2) can be expressed as:
\[ \text{Ratio} = \frac{A2 - A}{A - A1} = \frac{5}{10} \]

4. **Simplify the Ratio:**
- Simplifying \(\frac{5}{10}\) gives:
\[ \frac{5}{10} = \frac{1}{2} \]

5. **Conclusion:**
- Therefore, the ratio of the number of students in the first class to the number of students in the second class is:
\[ \text{Ratio} = 1 : 2 \]

### Final Answer:
The ratio of the students of the first class to the students of the second class is **1 : 2**.