Let the number of officers be \(x\).
And number of workers be = \((400 - x)\).
\(\Rightarrow\;\)\(3000 400 = 10,000 x + 2000 (400 - x)\)
\(\Rightarrow\;\)\(1200000 = 10000x + 800000 - 2000x\)
\(\Rightarrow\;\)\(1200000 - 800000 = 8000x\)
\(\Rightarrow\;\)\(400000 = 8000x\)
\(\Rightarrow\;\)x = \(\frac{400000}{8000}\)
\(\Rightarrow\;\)\(x = 50\)
Number of officers = \(50\)
Number of workers = \(400 - 50 = 350\)
The correct option is (A): 50, 350