Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in $1 \; \text{year},$ Akbar and Anthony can complete in $16$ months, Anthony and Amar can complete in $2 \; \text{years}.$ If the person who is neither the faster nor the slowest works alone, the time in months he will take to complete the project is

Let the efficiency of Amar, Akbar, and Anthony be $x, y$, and $z\;\text{units/month}.$

Now, $x+y+y+z+z+x = 4+3+2$

$\Rightarrow 2(x+y+z) = 9$

$\Rightarrow \boxed{x+y+z = 4.5}$

Now, we can calculate the individual efficiency.

The efficiency of Amar $x = 4.5-3 = 1.5$

The efficiency of Akbar $y = 4.5-2 = 2.5$

The efficiency of Anthony $z = 4.5-4 = 0.5$

We can say that Anthony is the slowest, Akbar is the fastest.

$\therefore$ The Person who is neither the fastest nor the slowest (Amar) works alone, the time is taken by him to complete the project $= \frac{48\; \text{units}}{1.5\;\text{units/month}} = 32\; \text{months}.$