In a factory, workers work in three shifts, say shift 1, shift 2 and shift 3 and they get wages in the ratio `3:4:8` depending on the shift 1, 2 and 3 respectively. Number of workers in the shifts are in the ratio `3:2:5`. If the total number of workers working is 1500 and wages per worker in shift 1 is Rs. 300, then the mean wage of a worker is

Options

A. Rs. 460
B. Rs. 520
C. Rs. 570
D. Rs. 420

Answer

To find the mean wage of a worker in the factory, we will follow these steps:

### Step 1: Determine the wages per worker for each shift
Given the wage ratio for the shifts is \(3:4:8\) and the wage per worker in shift 1 is Rs. 300, we can express the wages for each shift in terms of a variable \(x\):

- Wage in Shift 1: \(3x\)
- Wage in Shift 2: \(4x\)
- Wage in Shift 3: \(8x\)

Since \(3x = 300\), we can solve for \(x\):

\[ x = \frac{300}{3} = 100 \]

Now we can find the wages for shifts 2 and 3:

- Wage in Shift 2: \(4x = 4 \times 100 = 400\)
- Wage in Shift 3: \(8x = 8 \times 100 = 800\)

### Step 2: Determine the number of workers in each shift
The number of workers in the shifts is given in the ratio \(3:2:5\). Let the number of workers in each shift be represented as:

- Workers in Shift 1: \(3y\)
- Workers in Shift 2: \(2y\)
- Workers in Shift 3: \(5y\)

The total number of workers is 1500, so we can set up the equation:

\[ 3y + 2y + 5y = 1500 \]

This simplifies to:

\[ 10y = 1500 \]

Solving for \(y\):

\[ y = \frac{1500}{10} = 150 \]

Now we can find the number of workers in each shift:

- Workers in Shift 1: \(3y = 3 \times 150 = 450\)
- Workers in Shift 2: \(2y = 2 \times 150 = 300\)
- Workers in Shift 3: \(5y = 5 \times 150 = 750\)

### Step 3: Calculate the total wages for each shift
Now we can calculate the total wages paid to workers in each shift:

- Total wages in Shift 1: \(450 \times 300 = 135000\)
- Total wages in Shift 2: \(300 \times 400 = 120000\)
- Total wages in Shift 3: \(750 \times 800 = 600000\)

### Step 4: Calculate the mean wage
To find the mean wage, we need to calculate the total wages and divide it by the total number of workers:

Total wages:

\[ 135000 + 120000 + 600000 = 855000 \]

Total number of workers:

\[ 450 + 300 + 750 = 1500 \]

Now we can calculate the mean wage:

\[ \text{Mean Wage} = \frac{\text{Total Wages}}{\text{Total Workers}} = \frac{855000}{1500} = 570 \]

### Final Answer
The mean wage of a worker is Rs. 570.

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