The ratio of number of girls to number of boys is 1:2. If the average weight of the boys is 30 kg and the average weight of both the boys and the girls be 25 kg, then the average weight of the girls is:

Options

A. 15
B. 20
C. 35
D. 40

Answer

To solve the problem step by step, we can use the concept of alligation.

### Step 1: Understand the given information
- The ratio of the number of girls to boys is 1:2.
- The average weight of boys is 30 kg.
- The average weight of both boys and girls combined is 25 kg.

### Step 2: Assign variables based on the ratio
Let the number of girls be \( G \) and the number of boys be \( B \). According to the ratio:
- \( G = 1x \)
- \( B = 2x \) for some value \( x \).

### Step 3: Calculate the total weight of boys and the combined average weight
The total weight of boys can be calculated as:
- Total weight of boys = Average weight of boys × Number of boys
- Total weight of boys = \( 30 \, \text{kg} \times 2x = 60x \, \text{kg} \).

The combined average weight of boys and girls is given as 25 kg. Therefore, the total weight of both boys and girls can be expressed as:
- Total weight of both = Average weight × Total number of students
- Total weight of both = \( 25 \, \text{kg} \times (G + B) = 25 \, \text{kg} \times (1x + 2x) = 25 \, \text{kg} \times 3x = 75x \, \text{kg} \).

### Step 4: Set up the equation
Now we can set up the equation based on the total weights:
- Total weight of boys + Total weight of girls = Total weight of both
- \( 60x + \text{(Total weight of girls)} = 75x \).

### Step 5: Calculate the total weight of girls
Let the average weight of girls be \( G_w \). The total weight of girls can be expressed as:
- Total weight of girls = Average weight of girls × Number of girls
- Total weight of girls = \( G_w \times 1x = G_w \, x \).

Now substituting this into the equation:
- \( 60x + G_w \, x = 75x \).

### Step 6: Solve for \( G_w \)
Rearranging the equation gives:
- \( G_w \, x = 75x - 60x \)
- \( G_w \, x = 15x \).

Dividing both sides by \( x \) (assuming \( x \neq 0 \)):
- \( G_w = 15 \, \text{kg} \).

### Conclusion
The average weight of the girls is **15 kg**.

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