Study the information carefully to answer the questions that follows. In an annual function, 504 children participated. The ratio of number of girls to the number of boys is `5:3` respectively. Out of the total girls, 20% participated in dance and remaining girls participated in solo song, group song and drama in the ratio of `2:3:4` respectively. Two -third of the total boys participated in group song and remaining boys participated in solo song and dance in the ratio of `4:5` respectively.
What is the approximate percentage of the girls participated in solo song out of all the total participants ?

Options

A. `11%`
B. `15%`
C. `6%`
D. `20%`

Answer

To solve the problem step by step, we will follow the information provided in the question.

### Step 1: Calculate the total number of girls and boys.
The ratio of girls to boys is given as 5:3. Let the number of girls be \(5x\) and the number of boys be \(3x\).

The total number of children is:
\[ 5x + 3x = 504 \]
This simplifies to:
\[ 8x = 504 \]
Now, solve for \(x\):
\[ x = \frac{504}{8} = 63 \]

Now, calculate the number of girls and boys:
- Number of girls = \(5x = 5 \times 63 = 315\)
- Number of boys = \(3x = 3 \times 63 = 189\)

### Step 2: Calculate the number of girls participating in dance.
20% of the total girls participated in dance. Therefore:
\[ \text{Girls in dance} = 20\% \text{ of } 315 = \frac{20}{100} \times 315 = 63 \]

### Step 3: Calculate the remaining girls and their participation in other activities.
The remaining girls who did not participate in dance:
\[ \text{Remaining girls} = 315 - 63 = 252 \]

These remaining girls participated in solo song, group song, and drama in the ratio of \(2:3:4\). Let the common multiple be \(x\). Then:
\[ 2x + 3x + 4x = 252 \]
This simplifies to:
\[ 9x = 252 \]
Now, solve for \(x\):
\[ x = \frac{252}{9} = 28 \]

Now calculate the number of girls in each activity:
- Solo song = \(2x = 2 \times 28 = 56\)
- Group song = \(3x = 3 \times 28 = 84\)
- Drama = \(4x = 4 \times 28 = 112\)

### Step 4: Calculate the number of boys participating in group song.
Two-thirds of the total boys participated in group song:
\[ \text{Boys in group song} = \frac{2}{3} \times 189 = 126 \]

### Step 5: Calculate the remaining boys and their participation in other activities.
The remaining boys who did not participate in group song:
\[ \text{Remaining boys} = 189 - 126 = 63 \]

These remaining boys participated in solo song and dance in the ratio of \(4:5\). Let the common multiple be \(y\). Then:
\[ 4y + 5y = 63 \]
This simplifies to:
\[ 9y = 63 \]
Now, solve for \(y\):
\[ y = \frac{63}{9} = 7 \]

Now calculate the number of boys in each activity:
- Solo song = \(4y = 4 \times 7 = 28\)
- Dance = \(5y = 5 \times 7 = 35\)

### Step 6: Calculate the total number of participants in solo song.
Total participants in solo song (girls + boys):
\[ \text{Total in solo song} = \text{Girls in solo song} + \text{Boys in solo song} = 56 + 28 = 84 \]

### Step 7: Calculate the approximate percentage of girls participating in solo song out of all participants.
The total number of participants is 504. The percentage of girls participating in solo song is:
\[ \text{Percentage} = \left(\frac{\text{Girls in solo song}}{\text{Total participants}}\right) \times 100 = \left(\frac{56}{504}\right) \times 100 \]
Calculating this gives:
\[ \text{Percentage} \approx 11.11\% \]

### Final Answer:
The approximate percentage of girls participating in solo song out of all total participants is **11.11%**.

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