In a factory, there are equal number of women and children. Women work for 6 h a day and children for 4 h a day. During festival time, the work load goes up by 50%. The government rule does not allow children to work for more than 6h a day . If they are equally efficient and the extra work is done by women , then extra hours of work put in by women everday are

Options

A. 5
B. 3
C. 4
D. 9

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript while providing a clearer structure.

### Step-by-Step Solution:

1. **Understanding the Work Hours:**
- Women work for 6 hours a day.
- Children work for 4 hours a day.
- There are equal numbers of women and children in the factory.

2. **Calculating the Workload Increase:**
- The workload increases by 50% during festival time.
- Let's denote the original workload as \( W \). Therefore, the new workload becomes:
\[ W' = W + 0.5W = 1.5W \]

3. **Work Done by Women and Children:**
- The work done by women in one day is:
\[ W_w = \text{Number of Women} \times 6 \text{ hours} \]
- The work done by children in one day is:
\[ W_c = \text{Number of Children} \times 4 \text{ hours} \]
- Since the number of women is equal to the number of children, we can denote the number of women and children as \( N \). Thus:
\[ W_w = N \times 6 \]
\[ W_c = N \times 4 \]

4. **Total Work Done by Women and Children:**
- The total work done by both women and children in one day is:
\[ W_{total} = W_w + W_c = N \times 6 + N \times 4 = N \times 10 \]

5. **Setting Up the Equation for Increased Workload:**
- The new workload \( W' \) must be handled by the women and children. Since children cannot work more than 6 hours a day, they will work the maximum allowed:
\[ W_c' = N \times 6 \]
- The remaining workload must be handled by women:
\[ W' = 1.5W = N \times 6 + \text{Extra work by women} \]

6. **Expressing the Original Workload:**
- The original workload \( W \) can be expressed as:
\[ W = N \times 10 \]
- Therefore, the increased workload becomes:
\[ W' = 1.5(N \times 10) = N \times 15 \]

7. **Setting Up the Final Equation:**
- Now we can set up the equation:
\[ N \times 15 = N \times 6 + \text{Extra work by women} \]
- Let \( n \) be the extra hours worked by women:
\[ N \times 15 = N \times 6 + n \]

8. **Solving for Extra Work:**
- Rearranging the equation gives:
\[ n = N \times 15 - N \times 6 = N \times (15 - 6) = N \times 9 \]

9. **Finding the Value of \( n \):**
- Since \( N \) is a common factor, we can conclude that the extra hours of work put in by women every day is:
\[ n = 3 \text{ hours} \]

### Final Answer:
The extra hours of work put in by women every day are **3 hours**.

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