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

Given:

The average monthly income of agricultural workers = S

The average monthly income of other workers = T

The number of agricultural workers is 11 times that of other workers.

Formula used:

Average income of all workers = \(\dfrac{\text{Total income of all workers}}{\text{Total number of workers}}\)

Calculation:

Let the number of other workers be N.

Then, the number of agricultural workers = 11N.

Total number of workers = 11N + N = 12N.

Total income of agricultural workers = 11N × S = 11NS.

Total income of other workers = N × T = NT.

Total income of all workers = 11NS + NT.

Average income of all workers = \(\dfrac{11NS + NT}{12N}\)

⇒ \(\dfrac{11S + T}{12}\)

∴ The correct answer is option 1.