a) 23 days
b) 37 days
c) $$37\frac{1}{2}$$ days
d) 40 days

Answer: c
Explanation:
$$\eqalign{ & {\text{Whole}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & = {20 \times \frac{5}{4}} = 25\,{\text{days}} \cr & {\text{Now}},\,\left( {1 – \frac{4}{5}} \right) \cr & \frac{1}{5}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}}\,{\text{3}}\,{\text{days}} \cr & {\text{Whole}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}} \cr & = \left( {3 \times 5} \right) = 15\,{\text{days}} \cr & {\text{A’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = \frac{1}{{25}}, \cr & \left( {{\text{A + B}}} \right)\,{\text{‘s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = \frac{1}{{15}} \cr & {\text{B’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} \cr & = {\frac{1}{{15}} – \frac{1}{{25}}} = \frac{4}{{150}} = \frac{2}{{75}} \cr & {\text{B}}\,\,{\text{alone}}\,{\text{would}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}} \cr & \frac{{75}}{2} = 37\frac{1}{2}\,{\text{days}} \cr} $$