A firm employing 30 workers and paying on an average Rs 500 is combined with another firm employing 20 workers paying on an average Rs 600. What is the average pay of the workers of the combined firm?

Options

A. Rs 540
B. Rs 550
C. Rs 560
D. Rs 580

Explanation

To find the average pay of the workers of the combined firm, we can follow these steps:

### Step 1: Calculate the total pay for the first firm.
The first firm employs 30 workers and pays an average of Rs 500.

\[ \text{Total Pay of Firm 1} = \text{Number of Workers} \times \text{Average Pay} = 30 \times 500 = 15000 \text{ Rs} \]

### Step 2: Calculate the total pay for the second firm.
The second firm employs 20 workers and pays an average of Rs 600.

\[ \text{Total Pay of Firm 2} = \text{Number of Workers} \times \text{Average Pay} = 20 \times 600 = 12000 \text{ Rs} \]

### Step 3: Calculate the total pay of the combined firm.
Now, we add the total pay of both firms to get the total pay of the combined firm.

\[ \text{Total Pay of Combined Firm} = \text{Total Pay of Firm 1} + \text{Total Pay of Firm 2} = 15000 + 12000 = 27000 \text{ Rs} \]

### Step 4: Calculate the total number of workers in the combined firm.
Now, we add the number of workers from both firms to get the total number of workers in the combined firm.

\[ \text{Total Workers in Combined Firm} = \text{Workers in Firm 1} + \text{Workers in Firm 2} = 30 + 20 = 50 \]

### Step 5: Calculate the average pay of the workers in the combined firm.
Finally, we calculate the average pay of the workers in the combined firm by dividing the total pay by the total number of workers.

\[ \text{Average Pay of Combined Firm} = \frac{\text{Total Pay of Combined Firm}}{\text{Total Workers in Combined Firm}} = \frac{27000}{50} = 540 \text{ Rs} \]

### Final Answer:
The average pay of the workers of the combined firm is Rs 540.

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