The average monthly income (in Rs) of certain agricultural workers is S and that of other workers is T. The number of agricultural workers is 11 times that of other workers. Then, the average monthly income (in Rs) of all the workers is :

Options

A. `(S + 11T)/12`
B. `(S +T)/12`
C. `(11S + T)/12`
D. `1/(11 S) + T`

Answer

To find the average monthly income of all the workers, we can follow these steps:

### Step 1: Define the Variables
Let:
- \( N \) = number of other workers
- Then, the number of agricultural workers = \( 11N \)

### Step 2: Calculate Total Income
The total income of agricultural workers:
- Total income from agricultural workers = \( 11N \times S = 11NS \)

The total income of other workers:
- Total income from other workers = \( N \times T = NT \)

### Step 3: Calculate Total Income of All Workers
Now, we can find the total income of all workers combined:
- Total income of all workers = Total income from agricultural workers + Total income from other workers
- Total income of all workers = \( 11NS + NT \)

### Step 4: Calculate Total Number of Workers
The total number of workers is:
- Total number of workers = Number of agricultural workers + Number of other workers
- Total number of workers = \( 11N + N = 12N \)

### Step 5: Calculate Average Monthly Income of All Workers
The average monthly income of all workers can be calculated using the formula:
\[ \text{Average Income} = \frac{\text{Total Income}}{\text{Total Number of Workers}} \]
Substituting the values we calculated:
\[ \text{Average Income} = \frac{11NS + NT}{12N} \]

### Step 6: Simplify the Expression
Now, we can simplify the expression:
\[ \text{Average Income} = \frac{N(11S + T)}{12N} \]
Since \( N \) is in both the numerator and denominator, we can cancel it out:
\[ \text{Average Income} = \frac{11S + T}{12} \]

### Final Answer
Thus, the average monthly income of all the workers is:
\[ \frac{11S + T}{12} \]

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