Study the information carefully to answer the questions that follow:
A school consisting of 1560 students has boys and girls in the ratio of 7:5. All the students are enrolled for different countries’ tours, viz Russia, Switzerland and Japan. One-fifth of the boys are enrolled for only Switzerland tour. Twenty per cent of the girls are enrolled for only Japan tour. Ten, per cent of the boys are enrolled for only Russia tour. Twenty four per cent of the girls are enrolled for both Russia and Switzerland tour together but not for Japan.. The number of the girls enrolled for only Russia tour is two hundred per cent of the boys enrolled for the same tour. One-thirteenth of the boys are enrolled for all the three tours together. The ratio of the boys enrolled for Switzerland and Japan tour together but not for Russia to the,girls enrolled for the same tour is 2 : 1. Ten per cent of the girls are enrolled for only Switzerland tour whereas eight per cent of the girls are enrolled for both Switzerland and Japan tour together but not for Russia tour. The remaining girls are enrolled for all the three tours together. The number of boys enrolled for Russia and Switzerland tour together but not for Japan tour is fifty per cent of the number of girls enrolled for the same. The remaining boys are enrolled for only Japan tour.
The number of girls enrolled for only Switzerland, only Russia and-only Japan tour together is what per cent of the number of boys together enrolled for- the same? (rounded off to two digits after decimal)

Options

A. 37.57
B. 57.29
C. 61.93
D. 55.22

Answer

To solve the problem step by step, we will break down the information provided and calculate the required values systematically.

### Step 1: Determine the number of boys and girls in the school.
Given that the total number of students is 1560 and the ratio of boys to girls is 7:5, we can set up the equation:

Let the number of boys be \( 7x \) and the number of girls be \( 5x \).

\[ 7x + 5x = 1560 \]
\[ 12x = 1560 \]
\[ x = \frac{1560}{12} = 130 \]

Now, substituting back to find the number of boys and girls:
\[ \text{Number of boys} = 7x = 7 \times 130 = 910 \]
\[ \text{Number of girls} = 5x = 5 \times 130 = 650 \]

### Step 2: Calculate the number of boys enrolled in various tours.
1. **Boys enrolled for only Switzerland tour**:
\[ \text{Boys for Switzerland} = \frac{1}{5} \times 910 = 182 \]

2. **Boys enrolled for only Russia tour**:
\[ \text{Boys for Russia} = 10\% \times 910 = 0.1 \times 910 = 91 \]

3. **Boys enrolled for all three tours**:
\[ \text{Boys for all three tours} = \frac{1}{13} \times 910 = 70 \]

### Step 3: Calculate the number of girls enrolled in various tours.
1. **Girls enrolled for only Japan tour**:
\[ \text{Girls for Japan} = 20\% \times 650 = 0.2 \times 650 = 130 \]

2. **Girls enrolled for both Russia and Switzerland (not Japan)**:
\[ \text{Girls for Russia + Switzerland} = 24\% \times 650 = 0.24 \times 650 = 156 \]

3. **Girls enrolled for only Russia tour**:
The number of girls enrolled for only Russia is 200% of the boys enrolled for Russia:
\[ \text{Girls for only Russia} = 2 \times 91 = 182 \]

4. **Girls enrolled for only Switzerland tour**:
\[ \text{Girls for only Switzerland} = 10\% \times 650 = 0.1 \times 650 = 65 \]

5. **Girls enrolled for both Switzerland and Japan (not Russia)**:
\[ \text{Girls for Switzerland + Japan} = 8\% \times 650 = 0.08 \times 650 = 52 \]

### Step 4: Calculate the remaining girls.
To find the remaining girls who are enrolled in all three tours, we sum the known values:
\[ \text{Total girls accounted for} = 65 + 130 + 182 + 156 + 52 = 585 \]
\[ \text{Remaining girls} = 650 - 585 = 65 \]

### Step 5: Calculate the number of boys enrolled for only Japan tour.
The remaining boys can be calculated as follows:
\[ \text{Total boys accounted for} = 182 + 91 + 70 + (Boys for Russia + Switzerland) + (Boys for Japan) \]
Let \( y \) be the boys enrolled for only Japan tour. The boys enrolled for Russia and Switzerland (not Japan) is given as:
\[ \text{Boys for Russia + Switzerland} = 0.5 \times \text{Girls for Russia + Switzerland} = 0.5 \times 156 = 78 \]
Now summing:
\[ 910 = 182 + 91 + 70 + 78 + y \]
\[ 910 = 421 + y \implies y = 910 - 421 = 489 \]

### Step 6: Calculate the percentage of girls enrolled for only Switzerland, only Russia, and only Japan tour together compared to the boys.
The total number of girls enrolled for only Switzerland, only Russia, and only Japan:
\[ \text{Total girls} = 65 + 182 + 130 = 377 \]
The total number of boys enrolled for only Switzerland, only Russia, and only Japan:
\[ \text{Total boys} = 182 + 91 + 489 = 762 \]
Now, we find the percentage:
\[ \text{Percentage} = \left( \frac{377}{762} \right) \times 100 \approx 49.5\% \]

### Final Answer:
The number of girls enrolled for only Switzerland, only Russia, and only Japan tour together is approximately **49.5%** of the number of boys enrolled for the same.