A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

Solution (By Examveda Team)

$$\eqalign{ & \left( {{\text{B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{9} + \frac{1}{{12}}} = \frac{7}{{36}} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{B}}\,{\text{and}}\,{\text{C}}\,{\text{in}}\,{\text{3}}\,{\text{days}} \cr & = {\frac{7}{{36}} \times 3} = \frac{7}{{12}} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{7}{{12}}} = \frac{5}{{12}} \cr & {\text{Now}},\,\frac{1}{{24}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & {\text{So}},\,\frac{5}{{12}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & {24 \times \frac{5}{{12}}} = 10\,{\text{days}} \cr} $$