During our campaign against child labour we have found that is three glass making factories A,B and C thre were total 33 children aged below 18 were involved. The ratio of male to female in A, B and C was 4:3,3:2 and 5:4 respectively.If the no. of female children working in the factories B and C be equal then find the no.of female children working factory A:

Options

A. a. 5
B. b. 2
C. c. 8
D. d. 6

Answer

To solve the problem step by step, we will follow the given information and use algebra to find the number of female children working in factory A.

### Step 1: Define Variables
Let:
- The number of male children in factory A = 4x
- The number of female children in factory A = 3x
- The number of male children in factory B = 3y
- The number of female children in factory B = 2y
- The number of male children in factory C = 5z
- The number of female children in factory C = 4z

### Step 2: Set Up the Equation for Total Children
According to the problem, the total number of children in factories A, B, and C is 33. Therefore, we can set up the equation:
\[ 4x + 3x + 3y + 2y + 5z + 4z = 33 \]
This simplifies to:
\[ 7x + 5y + 9z = 33 \]

### Step 3: Use the Condition for Female Children in B and C
We know that the number of female children in factories B and C is equal:
\[ 2y = 4z \]
From this, we can express y in terms of z:
\[ y = 2z \]

### Step 4: Substitute y in the Total Children Equation
Now, we substitute \( y = 2z \) into the total children equation:
\[ 7x + 5(2z) + 9z = 33 \]
This simplifies to:
\[ 7x + 10z + 9z = 33 \]
or
\[ 7x + 19z = 33 \]

### Step 5: Solve for x and z
Now, we need to express one variable in terms of the other. We can rearrange the equation:
\[ 7x = 33 - 19z \]
To find integer solutions, we can try different values for z.

### Step 6: Try Different Values for z
Let’s try \( z = 1 \):
\[ 7x = 33 - 19(1) \]
\[ 7x = 14 \]
\[ x = 2 \]

### Step 7: Calculate y
Now, substitute \( z = 1 \) back into the equation for y:
\[ y = 2z = 2(1) = 2 \]

### Step 8: Find the Number of Female Children in Factory A
Now we can find the number of female children in factory A:
\[ \text{Number of female children in A} = 3x = 3(2) = 6 \]

### Conclusion
Thus, the number of female children working in factory A is **6**.

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