The average weight of the boys in a class is 30kg and the average weight of girls in the same class is 20kg. If the average weight of the whole class is 23.25kg, what could be the possible strength of boys and girls respectively in the same class?

Options

A. 14 and 16
B. 13 and 27
C. 17 and 27
D. none of these

Answer

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

### Step 1: Understand the given data
- Average weight of boys (Wb) = 30 kg
- Average weight of girls (Wg) = 20 kg
- Average weight of the whole class (Wc) = 23.25 kg

### Step 2: Set up the alligation formula
We will use the alligation method to find the ratio of the number of boys (B) to the number of girls (G).

The formula for alligation is:
\[ \text{Ratio of boys to girls} = \frac{Wg - Wc}{Wb - Wc} \]

### Step 3: Calculate the differences
- Difference between the average weight of girls and the average weight of the class:
\[ Wg - Wc = 20 - 23.25 = -3.25 \text{ kg} \]
- Difference between the average weight of boys and the average weight of the class:
\[ Wb - Wc = 30 - 23.25 = 6.75 \text{ kg} \]

### Step 4: Set up the ratio
Now we can set up the ratio of boys to girls:
\[ \text{Ratio of boys to girls} = \frac{-3.25}{6.75} \]
Since we are interested in the absolute values for the ratio, we can ignore the negative sign:
\[ \text{Ratio of boys to girls} = \frac{3.25}{6.75} \]

### Step 5: Simplify the ratio
To simplify this ratio, we can divide both numbers by 3.25:
\[ \frac{3.25 \div 3.25}{6.75 \div 3.25} = \frac{1}{2.0769} \approx \frac{1}{2} \]
Thus, the ratio of boys to girls is approximately 1:2.

### Step 6: Assign variables for the number of boys and girls
Let the number of boys be \( B = x \) and the number of girls be \( G = 2x \).

### Step 7: Find the total number of students
The total number of students in the class is:
\[ B + G = x + 2x = 3x \]

### Step 8: Conclusion
Thus, the possible strength of boys and girls in the class can be expressed as:
- Number of boys = \( x \)
- Number of girls = \( 2x \)

If we assume \( x = 1 \), then:
- Number of boys = 1
- Number of girls = 2
- Total strength = 3

If we assume \( x = 2 \), then:
- Number of boys = 2
- Number of girls = 4
- Total strength = 6

This means the strength can be any multiple of 3, maintaining the ratio of 1:2.