a) 15 Days
b) 20 Days
c) 25 Days
d) 30 Days

Answer: c
Explanation:
$$\eqalign{ & \left( {{\text{A + B}}} \right){\text{‘s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = \frac{1}{{10}} \cr & {\text{C’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = \frac{1}{{50}} \cr & \left( {{\text{A + B + C}}} \right){\text{‘s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} \cr & = {\frac{1}{{10}} + \frac{1}{{50}}} = \frac{6}{{50}} = \frac{3}{{25}}……..\left( {\text{i}} \right) \cr & {\text{A’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} \cr & = \left( {{\text{B + C}}} \right){\text{‘s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}}\,……..\left( {{\text{ii}}} \right) \cr & {\text{From}}\,\left( {\text{i}} \right)\,{\text{and}}\,\left( {{\text{ii}}} \right){\text{,we}}\,{\text{get}}:2 \times \left( {{\text{A’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}}} \right) \cr & = \frac{3}{{25}} \cr & {\text{A’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = \frac{3}{{50}} \cr & {\text{B’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}}\left( {\frac{1}{{10}} – \frac{3}{{50}}} \right) \cr & = \frac{2}{{50}} = \frac{1}{{25}} \cr & {\text{B}}\,\,{\text{alone}}\,{\text{could}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{25}}\,{\text{days}} \cr} $$