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.)
The average quantity of type B clothes worked upon in both the weeks was 510 metre how many metres of type B clothes was worked upon in week 2 alone

Options

A. 450
B. 540
C. 480
D. 510

Answer

To solve the problem step by step, let's break down the information provided and derive the necessary values.

### Step 1: Understand the Information Given
- In Week 1, the total cloth worked upon (Type A + Type B) is 1140 meters.
- Let the quantity of Type A in Week 1 be \( X \) meters and Type B be \( Y \) meters.
- Therefore, we can write the equation:
\[ X + Y = 1140 \quad \text{(1)} \]

### Step 2: Analyze Week 2 Data
- In Week 2, the quantity of Type A is 120 meters more than in Week 1:
\[ \text{Type A in Week 2} = X + 120 \]
- The quantity of Type B in Week 2 is 60 meters less than in Week 1:
\[ \text{Type B in Week 2} = Y - 60 \]

### Step 3: Calculate Average Quantity of Type B
- The average quantity of Type B worked upon in both weeks is given as 510 meters:
\[ \frac{(Y) + (Y - 60)}{2} = 510 \]
- Simplifying this, we get:
\[ \frac{2Y - 60}{2} = 510 \]
\[ 2Y - 60 = 1020 \]
\[ 2Y = 1080 \]
\[ Y = 540 \quad \text{(2)} \]

### Step 4: Find the Quantity of Type B in Week 2
- Now that we have the value of \( Y \), we can find the quantity of Type B in Week 2:
\[ \text{Type B in Week 2} = Y - 60 = 540 - 60 = 480 \text{ meters} \]

### Step 5: Final Answer
The quantity of Type B cloth worked upon in Week 2 alone is:
\[ \boxed{480} \text{ meters} \]