The average salary per head of the entire staff of a small factory including the managers and technicians is Rs.5750. The average salary per head of the manager is Rs. 20000 and that of technicians is Rs. 5000. If there are four managers, then the number of technicians in the factory is:

76

The correct answer is Option (3) → 76

Let the number of technicians be $x$ and total number of staff be $x + 4$ (including 4 managers).

Total salary = Average × Number of staff = 5750(x + 4)

Total salary of managers = 4 × 20000 = 80000

Total salary of technicians = 5000 × x

Equation: $5750(x + 4) = 5000x + 80000$

$5750x + 23000 = 5000x + 80000$

$5750x - 5000x = 80000 - 23000$

$750x = 57000 \Rightarrow x = \frac{57000}{750} = 76$

Answer: 76 technicians