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 difference between the number of boys and girls who have participated in dance ?

Options

A. 63
B. 35
C. 28
D. 126

Answer

To solve the problem step by step, we will follow the information provided in the question and break it down systematically.

### Step 1: Determine the number of girls and boys
We know that the total number of children is 504 and the ratio of girls to boys is 5:3.

1. **Calculate the total parts in the ratio**:
\[ 5 + 3 = 8 \text{ parts} \]

2. **Calculate the number of girls**:
\[ \text{Number of girls} = \frac{5}{8} \times 504 = 315 \]

3. **Calculate the number of boys**:
\[ \text{Number of boys} = \frac{3}{8} \times 504 = 189 \]

### Step 2: Calculate the number of girls participating in dance
Out of the total girls, 20% participated in dance.

1. **Calculate the number of girls participating in dance**:
\[ \text{Girls in dance} = 20\% \text{ of } 315 = \frac{20}{100} \times 315 = 63 \]

2. **Calculate the remaining girls**:
\[ \text{Remaining girls} = 315 - 63 = 252 \]

### Step 3: Distribute the remaining girls among solo song, group song, and drama
The remaining girls participate in solo song, group song, and drama in the ratio of 2:3:4.

1. **Calculate the total parts in the ratio**:
\[ 2 + 3 + 4 = 9 \text{ parts} \]

2. **Calculate the number of girls in solo song**:
\[ \text{Girls in solo song} = \frac{2}{9} \times 252 = 56 \]

3. **Calculate the number of girls in group song**:
\[ \text{Girls in group song} = \frac{3}{9} \times 252 = 84 \]

4. **Calculate the number of girls in drama**:
\[ \text{Girls in drama} = \frac{4}{9} \times 252 = 112 \]

### Step 4: Calculate the number of boys participating in dance
Two-thirds of the total boys participated in group song.

1. **Calculate the number of boys in group song**:
\[ \text{Boys in group song} = \frac{2}{3} \times 189 = 126 \]

2. **Calculate the remaining boys**:
\[ \text{Remaining boys} = 189 - 126 = 63 \]

### Step 5: Distribute the remaining boys among solo song and dance
The remaining boys participate in solo song and dance in the ratio of 4:5.

1. **Calculate the total parts in the ratio**:
\[ 4 + 5 = 9 \text{ parts} \]

2. **Calculate the number of boys in solo song**:
\[ \text{Boys in solo song} = \frac{4}{9} \times 63 = 28 \]

3. **Calculate the number of boys in dance**:
\[ \text{Boys in dance} = \frac{5}{9} \times 63 = 35 \]

### Step 6: Calculate the difference between the number of boys and girls who participated in dance
1. **Difference**:
\[ \text{Difference} = \text{Girls in dance} - \text{Boys in dance} = 63 - 35 = 28 \]

### Final Answer
The difference between the number of boys and girls who have participated in dance is **28**.

---