The average monthly salary of all the employees in a factory is Rs. 8840. If the average salary of all the officers is Rs. 15000 and that of the remaining employees is Rs. 8000, then what is the percent age of the officers among the employees?

Options

A. A) 10%
B. B) 12%
C. C) 8 `1/3` %
D. D) 11%

Answer

To solve the problem step by step, we will use the concept of allegation to find the percentage of officers among the employees.

### Step 1: Identify the given information
- Average salary of all employees = Rs. 8840
- Average salary of officers = Rs. 15000
- Average salary of remaining employees = Rs. 8000

### Step 2: Set up the allegation
We will use the allegation method to find the ratio of officers to remaining employees.

1. Write the average salaries:
- Salary of officers: Rs. 15000
- Combined average salary of all employees: Rs. 8840
- Salary of remaining employees: Rs. 8000

2. Calculate the differences:
- Difference between the salary of officers and the combined average:
\[ 15000 - 8840 = 6160 \]
- Difference between the combined average and the salary of remaining employees:
\[ 8840 - 8000 = 840 \]

### Step 3: Set up the ratio
Using the differences calculated, we can set up the ratio of the number of officers to the number of remaining employees:
\[ \text{Ratio} = \frac{840}{6160} \]

### Step 4: Simplify the ratio
To simplify the ratio:
1. Divide both numbers by 80:
\[ \frac{840 \div 80}{6160 \div 80} = \frac{10.5}{77} \]
2. To make it easier, multiply both by 2 to eliminate the decimal:
\[ \frac{21}{154} \]
3. Further simplifying gives:
\[ \frac{3}{22} \]

### Step 5: Calculate the percentage of officers
Now we can find the percentage of officers among the total employees:
1. Total parts = 3 (officers) + 22 (remaining employees) = 25
2. Percentage of officers:
\[ \text{Percentage} = \left(\frac{3}{25}\right) \times 100 = 12\% \]

### Final Answer
The percentage of officers among the employees is **12%**.

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