There is a group of 5 boys and 2 girls. The two groups wording together can do four times as much work as a boy and a girl Ratio of working capacities of a boy and a girl is:

Options

A. `2:1`
B. `2:3`
C. `1:3`
D. `1:2`

Answer

To solve the problem, we need to find the ratio of the working capacities of a boy and a girl based on the information provided.

### Step-by-Step Solution:

1. **Define Variables**:
- Let the work done by one boy in one day be represented as \( x \).
- Let the work done by one girl in one day be represented as \( y \).

2. **Calculate Total Work Done by the Groups**:
- There are 5 boys, so the total work done by 5 boys in one day is \( 5x \).
- There are 2 girls, so the total work done by 2 girls in one day is \( 2y \).
- Therefore, the total work done by both groups together in one day is:
\[ 5x + 2y \]

3. **Calculate Work Done by One Boy and One Girl**:
- The work done by one boy and one girl together in one day is:
\[ x + y \]

4. **Set Up the Equation**:
- According to the problem, the total work done by the two groups together is four times the work done by one boy and one girl:
\[ 5x + 2y = 4(x + y) \]

5. **Expand the Right Side**:
- Expanding the right side gives:
\[ 5x + 2y = 4x + 4y \]

6. **Rearrange the Equation**:
- Rearranging the equation to isolate terms involving \( x \) and \( y \):
\[ 5x - 4x = 4y - 2y \]
- This simplifies to:
\[ x = 2y \]

7. **Find the Ratio**:
- The ratio of the working capacities of a boy to a girl can be expressed as:
\[ \frac{x}{y} = \frac{2y}{y} = 2 \]
- Therefore, the ratio of the working capacities of a boy to a girl is:
\[ 2:1 \]

### Final Answer:
The ratio of the working capacities of a boy and a girl is \( 2:1 \).