The efficiencies of Amar, Akbar, and Anthony are provided as follows:
Let \(x\), \(y\), and \(z\) represent the efficiencies of Amar, Akbar, and Anthony, respectively.
The given information translates to these equations:
Adding all three equations reveals a relationship between \(x\), \(y\), and \(z\):
\[ (x + y) + (y + z) + (z + x) = 112 + 116 + 124 \]
Simplification yields:
\[ 2(x + y + z) = 352 \]
Therefore:
\[ x + y + z = \frac{352}{2} = 332 \]
Individual efficiencies \(x\), \(y\), and \(z\) are found by combining the sum equation with the original ones:
The individual efficiencies are:
Amar's efficiency (\(x = 132\)) is neither the highest nor the lowest. Thus, Amar is the worker who is neither the fastest nor the slowest.
The time required for an individual to complete the project is the reciprocal of their efficiency:
\[ \text{Time} = \frac{1}{\text{Efficiency}} = \frac{1}{x} \]
Substituting \(x = 132\):
\[ \text{Time} = \frac{1}{132} \quad \Rightarrow \quad \text{Time} = 32 \text{ months}. \]
Amar will complete the project independently in 32 months.