a) $$9\frac{1}{5}$$ days
b) $$9\frac{2}{7}$$ days
c) $$9\frac{3}{5}$$ days
d) 10

Answer: c
Explanation:
$$\eqalign{ & \left( {{\text{A + B + C}}} \right){\text{‘s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = \frac{1}{4} \cr & {\text{A’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = \frac{1}{{16}} \cr & {\text{B’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} = \frac{1}{{12}} \cr & {\text{C’s}}\,{\text{1}}\,{\text{day’s}}\,{\text{work}} \cr & = \frac{1}{4} – \left( {\frac{1}{{16}} + \frac{1}{{12}}} \right) = {\frac{1}{4} – \frac{7}{{48}}} = \frac{5}{{48}} \cr & {\text{C}}\,\,{\text{alone}}\,{\text{can}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}} \cr & \frac{{48}}{5} = 9\frac{3}{5}\,{\text{days}} \cr} $$