A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?

Solution(By Examveda Team)

$$\eqalign{ & {\text{2(A + B + C)'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{30}} + \frac{1}{{24}} + \frac{1}{{20}}} \cr & = \frac{{15}}{{120}} = \frac{1}{8} \cr & \therefore \left( {{\text{A + B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{{2 \times 8}} = \frac{1}{{16}} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{A,}}\,{\text{B,}}\,{\text{C}}\,{\text{in}}\,{\text{10}}\,{\text{days}} \cr & = \frac{{10}}{{16}} = \frac{5}{8} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{5}{8}} = \frac{3}{8} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{16}} - \frac{1}{{24}}} = \frac{1}{{48}} \cr & {\text{Now}},\,\frac{1}{{48}}\,{\text{work}}\,{\text{isdone}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & {\text{So}},\,\frac{3}{8}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}} \cr & {48 \times \frac{3}{8}} = 18\,{\text{days}} \cr} $$