In a school, the ratio of boys to girls is `4 : 3` and the ratio of girls to teachers is `8 : 1`. The ratio of students to teachers is:

Options

A. `56 : 3`
B. `55 : 1 `
C. `49 : 3`
D. `56 : 1`

Answer

To find the ratio of students to teachers given the ratios of boys to girls and girls to teachers, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Ratios**:
- The ratio of boys to girls (B:G) is given as \(4:3\).
- The ratio of girls to teachers (G:T) is given as \(8:1\).

2. **Express Boys and Girls in Terms of a Common Variable**:
- Let the number of boys be \(4x\) and the number of girls be \(3x\), where \(x\) is a common multiplier.

3. **Express Girls and Teachers in Terms of a Common Variable**:
- From the ratio of girls to teachers, we can express the number of girls as \(8y\) and the number of teachers as \(y\), where \(y\) is another common multiplier.

4. **Equate the Number of Girls**:
- Since both expressions represent the number of girls, we can set them equal to each other:
\[ 3x = 8y \]

5. **Solve for \(x\) in Terms of \(y\)**:
- Rearranging the equation gives:
\[ x = \frac{8y}{3} \]

6. **Substitute \(x\) Back to Find Boys and Girls**:
- Substitute \(x\) back into the expressions for boys and girls:
- Number of boys \(B = 4x = 4 \times \frac{8y}{3} = \frac{32y}{3}\)
- Number of girls \(G = 3x = 3 \times \frac{8y}{3} = 8y\)

7. **Find the Number of Teachers**:
- From the ratio of girls to teachers, we have:
- Number of teachers \(T = y\)

8. **Calculate Total Students**:
- Total students (B + G):
\[ B + G = \frac{32y}{3} + 8y = \frac{32y}{3} + \frac{24y}{3} = \frac{56y}{3} \]

9. **Form the Ratio of Students to Teachers**:
- Now we can form the ratio of students to teachers:
\[ \text{Ratio of students to teachers} = \frac{B + G}{T} = \frac{\frac{56y}{3}}{y} = \frac{56}{3} \]

10. **Final Ratio**:
- Therefore, the ratio of students to teachers is \(56:3\).

### Final Answer:
The ratio of students to teachers is \(56:3\).

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