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:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 76
Let the number of technicians be n. The total salary is the same whether it is found from the overall average or from the two groups:
\(5750(4 + n) = 20000 \times 4 + 5000n\)
\(23000 + 5750n = 80000 + 5000n\)
\(750n = 57000\)
\(n = 76\)
Shortcut: By alligation, technicians : managers = (20000 − 5750) : (5750 − 5000) = 14250 : 750 = 19 : 1. With 4 managers, there are \(19 \times 4 = 76\) technicians.
CBSE Applied Mathematics (Class XII):
Alligation and Mixture
