The mean weight of all the students in a certain class is 60 kg. The mean weight of the boys from the class is 70 kg. while that of the girls is 55 kg. What is the ratio of number of boys to that of girls?

Options

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

Explanation

To solve the problem, we need to find the ratio of the number of boys to the number of girls in the class based on their mean weights. Let's denote the number of boys as \( x \) and the number of girls as \( y \).

### Step-by-Step Solution:

1. **Understand the Mean Weight Formula**:
The mean weight of all students in the class is given as 60 kg. The formula for the mean weight is:
\[ \text{Mean Weight} = \frac{\text{Total Weight}}{\text{Total Number of Students}} \]
Therefore, we can express the total weight of all students as:
\[ \text{Total Weight} = \text{Mean Weight} \times \text{Total Number of Students} = 60 \times (x + y) \]

2. **Calculate Total Weight of Boys and Girls**:
The mean weight of boys is 70 kg, so the total weight of boys is:
\[ \text{Total Weight of Boys} = 70x \]
The mean weight of girls is 55 kg, so the total weight of girls is:
\[ \text{Total Weight of Girls} = 55y \]

3. **Set Up the Equation**:
The total weight of the class can also be expressed as the sum of the total weights of boys and girls:
\[ \text{Total Weight} = \text{Total Weight of Boys} + \text{Total Weight of Girls} = 70x + 55y \]
Now, we can set the two expressions for total weight equal to each other:
\[ 60(x + y) = 70x + 55y \]

4. **Expand and Rearrange the Equation**:
Expanding the left side gives:
\[ 60x + 60y = 70x + 55y \]
Rearranging the equation to isolate terms involving \( x \) and \( y \):
\[ 60y - 55y = 70x - 60x \]
Simplifying this gives:
\[ 5y = 10x \]

5. **Solve for the Ratio**:
Dividing both sides by 5, we get:
\[ y = 2x \]
This means the number of girls is twice the number of boys. To find the ratio of boys to girls, we express it as:
\[ \frac{x}{y} = \frac{x}{2x} = \frac{1}{2} \]
Therefore, the ratio of the number of boys to the number of girls is:
\[ \text{Ratio of Boys to Girls} = 1:2 \]

### Final Answer:
The ratio of the number of boys to the number of girls is \( 1:2 \).