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 total ratio of wages and workers
The wages are in the ratio \(3:4:8\) for shifts 1, 2, and 3 respectively. The total ratio is:
\[ 3 + 4 + 8 = 15 \]

### Step 2: Calculate the number of workers in each shift
The number of workers is in the ratio \(3:2:5\). The total number of workers is given as 1500. Therefore, we can find the number of workers in each shift as follows:

- For shift 1:
\[ \text{Workers in shift 1} = \frac{3}{3 + 2 + 5} \times 1500 = \frac{3}{10} \times 1500 = 450 \]

- For shift 2:
\[ \text{Workers in shift 2} = \frac{2}{10} \times 1500 = 300 \]

- For shift 3:
\[ \text{Workers in shift 3} = \frac{5}{10} \times 1500 = 750 \]

### Step 3: Calculate the wages for each shift
Given that the wage per worker in shift 1 is Rs. 300, we can find the wages for shifts 2 and 3 using the wage ratios.

- Wage in shift 2:
\[ \text{Wage in shift 2} = \frac{4}{3} \times 300 = 400 \]

- Wage in shift 3:
\[ \text{Wage in shift 3} = \frac{8}{3} \times 300 = 800 \]

### Step 4: Calculate the total wages for each shift
Now we can calculate the total wages paid in each shift:

- Total wages in shift 1:
\[ \text{Total wages in shift 1} = 450 \times 300 = 135000 \]

- Total wages in shift 2:
\[ \text{Total wages in shift 2} = 300 \times 400 = 120000 \]

- Total wages in shift 3:
\[ \text{Total wages in shift 3} = 750 \times 800 = 600000 \]

### Step 5: Calculate the overall total wages
Now, we can find the overall total wages paid to all workers:
\[ \text{Total wages} = 135000 + 120000 + 600000 = 855000 \]

### Step 6: Calculate the mean wage
Finally, we can calculate the mean wage of a worker:
\[ \text{Mean wage} = \frac{\text{Total wages}}{\text{Total number of workers}} = \frac{855000}{1500} = 570 \]

Thus, the mean wage of a worker is Rs. 570.

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