Directions (): Study the following information carefully and answer the given questions.
A designer studio, as a part of an assignment undertaken, had employed a certain number of workers for two weeks (Week 1 and Week 2), to work upon two types of cloth material (Type A and Type B). In week 1, the workers could work upon 1140 metres of cloth material (Type A Type B). The quantity of Type A material worked upon in week 2 was 120 metre more than that in week 1. The quantity of Type B material worked upon in week 2 was 60 metres less than that in week 1. The wage per worker given (for two weeks together) was 12000. The total wages paid to workers for both the weeks together was 14,40,000. (The same number of workers were working in week 1 and week 2.)
If the number of male workers was 24 more than that of female workers how many female workers were working?

Options

A. 72
B. 36
C. 48
D. 42

Answer

To solve the problem step by step, let's break down the information provided:

1. **Understanding the Total Work Done in Week 1**:
- In Week 1, the total amount of cloth worked upon (Type A + Type B) is 1140 metres.

2. **Establishing Variables for Week 1**:
- Let the quantity of Type A cloth worked upon in Week 1 be \( x \) metres.
- Therefore, the quantity of Type B cloth worked upon in Week 1 will be \( 1140 - x \) metres.

3. **Understanding the Work Done in Week 2**:
- In Week 2, the quantity of Type A cloth worked upon is 120 metres more than in Week 1:
\[ \text{Type A in Week 2} = x + 120 \]
- The quantity of Type B cloth worked upon in Week 2 is 60 metres less than in Week 1:
\[ \text{Type B in Week 2} = (1140 - x) - 60 = 1080 - x \]

4. **Setting Up the Total Work for Week 2**:
- The total work done in Week 2 can be expressed as:
\[ (x + 120) + (1080 - x) = 1200 \text{ metres} \]

5. **Calculating the Number of Workers**:
- The total wages paid to workers for both weeks is given as ₹14,40,000.
- The wage per worker for two weeks is ₹12,000.
- Therefore, the total number of workers can be calculated as:
\[ \text{Number of workers} = \frac{14,40,000}{12,000} = 120 \]

6. **Establishing the Relationship Between Male and Female Workers**:
- Let the number of female workers be \( f \).
- Then, the number of male workers will be \( f + 24 \).
- The total number of workers is given as 120:
\[ f + (f + 24) = 120 \]
- Simplifying this equation:
\[ 2f + 24 = 120 \]
\[ 2f = 120 - 24 \]
\[ 2f = 96 \]
\[ f = 48 \]

7. **Conclusion**:
- The number of female workers is \( 48 \).

### Final Answer:
The number of female workers working is **48**.