If the average weight of a class of students is 15 and the average weight of another class of students is 30, then 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, we need to find the ratio of the number of students in the first class (Class A) to the number of students in the second class (Class B) given their average weights and the combined average weight.

### Step-by-step Solution:

1. **Define Variables:**
Let the number of students in Class A be \( x \) and the number of students in Class B be \( y \).

2. **Set Up the Average Weight Equation:**
The average weight of Class A is 15, and the average weight of Class B is 30. The combined average weight of both classes is given as 25. The equation for the combined average weight can be set up as follows:
\[ \frac{(15x + 30y)}{(x + y)} = 25 \]

3. **Cross Multiply to Eliminate the Fraction:**
To eliminate the fraction, we can cross-multiply:
\[ 15x + 30y = 25(x + y) \]

4. **Expand the Right Side:**
Expanding the right side gives:
\[ 15x + 30y = 25x + 25y \]

5. **Rearrange the Equation:**
Now, we can rearrange the equation to isolate terms involving \( x \) and \( y \):
\[ 15x + 30y - 25x - 25y = 0 \]
This simplifies to:
\[ -10x + 5y = 0 \]

6. **Solve for the Ratio:**
Rearranging the equation gives:
\[ 10x = 5y \implies \frac{x}{y} = \frac{5}{10} = \frac{1}{2} \]

7. **Conclusion:**
Therefore, the ratio of the number of students in Class A to the number of students in Class B is:
\[ x : y = 1 : 2 \]

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

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