A factory employs skilled workers, unskilled workers and clerks in the proportion 8 : 5 : 1 and the wages of a skilled worker, an unskilled worker and a clerk are in the ratio 5 : 2 : 3. When 20 unskilled workers are employed, the total daily wages of all amount to Rs 3180. Find the daily wages paid to each category of employees.

Options

A. `2100, 800, 280`
B. `2400, 480, 300`
C. `2400, 600, 180`
D. `2200, 560, 420`

Answer

To solve the problem step-by-step, we will follow the given ratios and information to find the daily wages paid to each category of employees.

### Step 1: Understand the Ratios
The factory employs skilled workers, unskilled workers, and clerks in the ratio of 8:5:1. This means for every 8 skilled workers, there are 5 unskilled workers and 1 clerk.

### Step 2: Determine the Number of Workers
Given that there are 20 unskilled workers, we can find the number of skilled workers and clerks based on the ratio.

- Let the number of skilled workers be \( 8k \), unskilled workers be \( 5k \), and clerks be \( k \).
- Since we know there are 20 unskilled workers:
\[ 5k = 20 \implies k = 4 \]
- Therefore, the number of skilled workers is:
\[ 8k = 8 \times 4 = 32 \]
- The number of clerks is:
\[ k = 4 \]

### Step 3: Understand the Wages Ratios
The wages of skilled workers, unskilled workers, and clerks are in the ratio of 5:2:3. Let the wages be represented as:
- Skilled worker's wage = \( 5x \)
- Unskilled worker's wage = \( 2x \)
- Clerk's wage = \( 3x \)

### Step 4: Calculate Total Wages
Now, we can express the total wages for each category of workers:
- Total wages for skilled workers:
\[ \text{Total Skilled Wages} = 32 \times 5x = 160x \]
- Total wages for unskilled workers:
\[ \text{Total Unskilled Wages} = 20 \times 2x = 40x \]
- Total wages for clerks:
\[ \text{Total Clerk Wages} = 4 \times 3x = 12x \]

### Step 5: Set Up the Equation
The total daily wages of all employees amount to Rs 3180. Therefore, we can set up the equation:
\[ 160x + 40x + 12x = 3180 \]
Combining the terms gives:
\[ 212x = 3180 \]

### Step 6: Solve for \( x \)
To find \( x \), we divide both sides by 212:
\[ x = \frac{3180}{212} = 15 \]

### Step 7: Calculate Daily Wages for Each Category
Now that we have \( x = 15 \), we can calculate the daily wages for each category:
- Skilled worker's wage:
\[ 5x = 5 \times 15 = 75 \text{ Rs} \]
- Unskilled worker's wage:
\[ 2x = 2 \times 15 = 30 \text{ Rs} \]
- Clerk's wage:
\[ 3x = 3 \times 15 = 45 \text{ Rs} \]

### Step 8: Calculate Total Daily Wages
Finally, we can calculate the total daily wages for each category:
- Total daily wages for skilled workers:
\[ 32 \times 75 = 2400 \text{ Rs} \]
- Total daily wages for unskilled workers:
\[ 20 \times 30 = 600 \text{ Rs} \]
- Total daily wages for clerks:
\[ 4 \times 45 = 180 \text{ Rs} \]

### Final Result
- Daily wages for skilled workers: **Rs 2400**
- Daily wages for unskilled workers: **Rs 600**
- Daily wages for clerks: **Rs 180**

---