a) 6 Days
b) 10 Days
c) 15 Days
d) 20 Days

Answer: b
Explanation:
$$\eqalign{ & {\text{work}}\,{\text{done}}\,{\text{by}}\,{\text{X}}\,{\text{in}}\,{\text{4}}\,{\text{days}} \cr & = {\frac{1}{{20}} \times 4} = \frac{1}{5} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 – \frac{1}{5}} = \frac{4}{5} \cr & \left( {{\text{X + Y}}} \right){\text{‘s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} \cr & = {\frac{1}{{20}} + \frac{1}{{12}}} = \frac{8}{{60}} = \frac{2}{{15}} \cr & \frac{2}{{15}}{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{X}}\,{\text{and}}\,{\text{Y}}\,{\text{in}}\,{\text{1}}\,{\text{day}}. \cr & \,\frac{4}{5}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{X}}\,{\text{and}}\,{\text{Y}}\,{\text{in}} \cr & {\frac{{15}}{2} \times \frac{4}{5}} = 6\,{\text{days}} \cr & {\text{Hence,}}\,{\text{total}}\,{\text{time}}\,{\text{taken}} \cr & = \left( {6 + 4} \right)\,{\text{days}} \cr & = 10\,{\text{days}} \cr} $$