The average monthly income (in Rs.) of male employees of a company is P and that of female employees is Q. If the number of male employees is 11 times that of female employees, then the average monthly income (in Rs.) of all the employees is

Options

A. `(P+Q)/(2)`
B. `(P+11Q)/(2)`
C. `(1)/(11P)+Q`
D. `(11P+Q)/(12)`

Answer

To find the average monthly income of all employees in the company, we can follow these steps:

### Step 1: Define Variables
Let:
- \( n_f \) = number of female employees
- \( n_m \) = number of male employees = \( 11 \times n_f \)
- \( P \) = average monthly income of male employees
- \( Q \) = average monthly income of female employees

### Step 2: Calculate Total Income
The total income of male employees can be calculated as:
\[ \text{Total income of males} = n_m \times P = (11 \times n_f) \times P = 11n_fP \]

The total income of female employees can be calculated as:
\[ \text{Total income of females} = n_f \times Q \]

### Step 3: Calculate Total Income of All Employees
Now, we can find the total income of all employees:
\[ \text{Total income of all employees} = \text{Total income of males} + \text{Total income of females} = 11n_fP + n_fQ \]

### Step 4: Calculate Total Number of Employees
The total number of employees is:
\[ \text{Total number of employees} = n_m + n_f = 11n_f + n_f = 12n_f \]

### Step 5: Calculate Average Monthly Income of All Employees
The average monthly income of all employees can be calculated as:
\[ \text{Average income} = \frac{\text{Total income of all employees}}{\text{Total number of employees}} = \frac{11n_fP + n_fQ}{12n_f} \]

### Step 6: Simplify the Expression
We can simplify the expression:
\[ \text{Average income} = \frac{n_f(11P + Q)}{12n_f} = \frac{11P + Q}{12} \]

Thus, the average monthly income of all employees is:
\[ \text{Average income} = \frac{11P + Q}{12} \]

### Final Answer
The average monthly income of all employees is \(\frac{11P + Q}{12}\).

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