1/5 of boys and 1/4 of girls of a class participated in swimming while 2/3 of boys and 3/5 of girls participated in sports .If total number of student in the class was 65 how many girls participated in sports

Options

A. 12
B. 4
C. 16
D. Data inadequate

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information given.

### Step 1: Define the Variables
Let:
- \( B \) = number of boys in the class
- \( G \) = number of girls in the class

### Step 2: Set Up the Total Students Equation
According to the problem, the total number of students in the class is 65:
\[ B + G = 65 \]

### Step 3: Set Up the Swimming Participation Equation
From the problem, we know that:
- \( \frac{1}{5} \) of boys participated in swimming: \( \frac{1}{5}B \)
- \( \frac{1}{4} \) of girls participated in swimming: \( \frac{1}{4}G \)

### Step 4: Set Up the Sports Participation Equation
We also know that:
- \( \frac{2}{3} \) of boys participated in sports: \( \frac{2}{3}B \)
- \( \frac{3}{5} \) of girls participated in sports: \( \frac{3}{5}G \)

### Step 5: Calculate the Total Participants in Swimming
The total number of students who participated in swimming is:
\[ \frac{1}{5}B + \frac{1}{4}G \]

### Step 6: Calculate the Total Participants in Sports
The total number of students who participated in sports is:
\[ \frac{2}{3}B + \frac{3}{5}G \]

### Step 7: Solve the Equations
We have two equations:
1. \( B + G = 65 \)
2. We can express \( G \) in terms of \( B \): \( G = 65 - B \)

Substituting \( G \) in the swimming equation:
\[ \frac{1}{5}B + \frac{1}{4}(65 - B) \]

Now, we can simplify this equation and solve for \( B \) and \( G \).

### Step 8: Substitute and Simplify
Substituting \( G \):
\[ \frac{1}{5}B + \frac{1}{4}(65 - B) = \frac{1}{5}B + \frac{65}{4} - \frac{1}{4}B \]
Finding a common denominator (20):
\[ \frac{4}{20}B + \frac{325}{20} - \frac{5}{20}B = \frac{-1}{20}B + \frac{325}{20} \]

### Step 9: Solve for \( B \)
Now we can set up the equation for sports participation:
\[ \frac{2}{3}B + \frac{3}{5}(65 - B) \]
Again, we can simplify this equation and solve for \( B \) and \( G \).

### Step 10: Calculate Girls Participating in Sports
Once we have the values of \( B \) and \( G \), we can find the number of girls participating in sports:
\[ \text{Girls in Sports} = \frac{3}{5}G \]

### Final Calculation
Now, we can calculate the values and find out how many girls participated in sports.