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

Options

A. 14 and 26
B. 13 and 27
C. 17 and 27
D. none of these

Answer

To solve the problem, we will use the concept of alligation to find the possible strength of boys and girls in the class.

### Step 1: Define the variables
Let:
- \( b \) = number of boys
- \( g \) = number of girls

### Step 2: Set up the average weight equations
We know the average weights:
- Average weight of boys = 30 kg
- Average weight of girls = 20 kg
- Average weight of the whole class = 23.25 kg

The total weight of boys can be expressed as \( 30b \) and the total weight of girls as \( 20g \).

### Step 3: Write the equation for the average weight of the whole class
The average weight of the whole class can be expressed as:
\[ \frac{30b + 20g}{b + g} = 23.25 \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 30b + 20g = 23.25(b + g) \]

### Step 5: Expand the equation
Expanding the right side:
\[ 30b + 20g = 23.25b + 23.25g \]

### Step 6: Rearrange the equation
Rearranging the terms gives:
\[ 30b - 23.25b = 23.25g - 20g \]
\[ 6.75b = 3.25g \]

### Step 7: Simplify the equation
Dividing both sides by 3.25:
\[ \frac{b}{g} = \frac{3.25}{6.75} = \frac{13}{27} \]

### Step 8: Set the ratio for boys and girls
This means the ratio of boys to girls is 13:27. Let’s assume \( b = 13k \) and \( g = 27k \) for some integer \( k \).

### Step 9: Find the total strength
The total strength of the class would be:
\[ b + g = 13k + 27k = 40k \]

### Step 10: Determine possible values for \( k \)
Since \( b \) and \( g \) must be whole numbers, \( k \) can be any positive integer. Therefore, the possible strengths of boys and girls can be expressed as:
- Boys = \( 13k \)
- Girls = \( 27k \)

### Conclusion
For \( k = 1 \):
- Boys = 13
- Girls = 27

For \( k = 2 \):
- Boys = 26
- Girls = 54

And so on. Thus, the possible strengths of boys and girls in the class can be any multiples of 13 and 27 respectively.

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