Let W represent the total work. Let g and s be the work efficiencies of Gautam and Suhani, respectively.
According to the problem statement:
$ \Rightarrow\ g + s = \frac{W}{20} $ (combined work per day) ……. (i)
Gautam works at 60% of his efficiency ($ \frac{3g}{5} $), and Suhani works at 150% of her efficiency ($ \frac{3s}{2} $).
Using these adjusted efficiencies, the combined work per day is:
$ \Rightarrow\ \frac{3g}{5} + \frac{3s}{2} = \frac{W}{20} $ (combined work per day)
Equating the two expressions for combined work per day:
$ \Rightarrow\ g + s = \frac{3g}{5} + \frac{3s}{2} $
Solving for the ratio of their efficiencies:
$ \Rightarrow\ \frac{s}{g} = \frac{4}{5} $
This indicates that Gautam is more efficient than Suhani.
Substituting the relationship $ s = \frac{4g}{5} $ into equation (i):
$ \Rightarrow\ g + \frac{4g}{5} = \frac{W}{20} $
Simplifying the left side:
$ \Rightarrow\ \frac{9}{5}g = \frac{W}{20} $
Solving for Gautam's individual efficiency:
$ \Rightarrow\ g = \frac{W}{36} $
Therefore, Gautam requires 36 days to complete the entire work.
The correct option is (B) : 36.