Read the following information carefully to answer the questions given below?
Five schools A,B, C, D and E participatd in the programme of a game. The total number of students are 800 in this programme. The ratio between the number of girls and boy is `1:3` respectively 25% out of total students are from school B. 110 students out of the total number of students are from school D 10% studetns out of the total are from school C. The number of students in school A are double to the number of students is school D. Remaining students are in school E. 30% of the total students in school B are girls. The half number of girls students in B is equal to teh number of girls in school D. 10% students of school A is equal to the number of girls in the school C. The number of girls in school A and E are equal.
What is the approximate percentage of the total number of girls in school D to the total number of students in school A?

Options

A. 10
B. 20
C. 12
D. 14

Answer

To solve the problem step by step, we will analyze the information given and calculate the required values systematically.

### Step 1: Determine the total number of girls and boys
The total number of students is 800. The ratio of girls to boys is 1:3.

Let the number of girls be \( G \) and the number of boys be \( B \).

From the ratio:
\[ G : B = 1 : 3 \]
This means:
\[ G = \frac{1}{4} \times 800 = 200 \quad \text{(girls)} \]
\[ B = \frac{3}{4} \times 800 = 600 \quad \text{(boys)} \]

### Step 2: Calculate the number of students in each school
- **School B**: 25% of total students
\[ \text{Students in B} = 0.25 \times 800 = 200 \]

- **School D**: Given directly
\[ \text{Students in D} = 110 \]

- **School C**: 10% of total students
\[ \text{Students in C} = 0.10 \times 800 = 80 \]

- **School A**: The number of students in A is double that of D
\[ \text{Students in A} = 2 \times 110 = 220 \]

- **School E**: Remaining students
\[ \text{Students in E} = 800 - (200 + 110 + 80 + 220) = 800 - 620 = 180 \]

### Step 3: Calculate the number of girls in each school
- **School B**: 30% of students in B are girls
\[ \text{Girls in B} = 0.30 \times 200 = 60 \]

- **School D**: Half the number of girls in B equals the number of girls in D
\[ \text{Girls in D} = \frac{1}{2} \times 60 = 30 \]

- **School C**: Let \( x \) be the number of girls in C. 10% of students in A equals the number of girls in C.
\[ 0.10 \times 220 = x \implies x = 22 \quad \text{(Girls in C)} \]

- **School A**: Let \( y \) be the number of girls in A. The number of girls in A and E are equal.
\[ \text{Girls in A} = y \]
\[ \text{Girls in E} = y \]

### Step 4: Calculate total girls
From the total number of girls:
\[ G = 200 = \text{Girls in A} + \text{Girls in B} + \text{Girls in C} + \text{Girls in D} + \text{Girls in E} \]
Substituting the known values:
\[ 200 = y + 60 + 22 + 30 + y \]
\[ 200 = 2y + 112 \]
\[ 2y = 200 - 112 = 88 \implies y = 44 \]

### Step 5: Find the number of girls in each school
- **Girls in A**: 44
- **Girls in E**: 44
- **Girls in B**: 60
- **Girls in C**: 22
- **Girls in D**: 30

### Step 6: Calculate the percentage of girls in school D to the total number of students in school A
We need to find the percentage of girls in school D compared to the total number of students in school A:
\[ \text{Percentage} = \left( \frac{\text{Girls in D}}{\text{Total Students in A}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage} = \left( \frac{30}{220} \right) \times 100 \approx 13.64\% \]

### Final Answer
The approximate percentage of the total number of girls in school D to the total number of students in school A is **approximately 14%**.