A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

Explanation:-

$$\eqalign{ & {\text{A's}}\,{\text{2}}\,{\text{day's}}\,{\text{work}} = \left( {\frac{1}{{20}} \times 2} \right) = \frac{1}{{10}} \cr & \left( {{\text{A + B + C}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {\frac{1}{{20}} + \frac{1}{{30}} + \frac{1}{{60}}} \right) = \frac{6}{{60}} = \frac{1}{{10}} \cr & {\text{Work}}\,{\text{done}}\,{\text{in}}\,{\text{3}}\,{\text{days}} = \left( {\frac{1}{{10}} + \frac{1}{{10}}} \right) = \frac{1}{5} \cr & {\text{Now}},\,\frac{1}{5}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{in}}\,{\text{3}}\,{\text{dys}} \cr & \therefore {\text{Whole}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{in}}\, \cr & \left( {3 \times 5} \right) = 15\,{\text{days}} \cr}$$