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A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :

Correct Answer: 12 days
$$\eqalign{ & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{1}{{15}} + \frac{1}{{10}}} = \frac{1}{6} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}}\,{\text{in}}\,{\text{2}}\,{\text{days}} \cr & = {\frac{1}{6} \times 2} = \frac{1}{3} \cr & {\text{Remaining}}\,{\text{work}} \cr & = {1 - \frac{1}{3}} = \frac{2}{3} \cr & {\text{Now}},\,\frac{1}{{15}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{A}}\,{\text{in}}\,{\text{1}}\,{\text{day}} \cr & \therefore \frac{2}{3}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{a}}\,{\text{in}} \cr & {15 \times \frac{2}{3}} = 10\,{\text{days}} \cr & {\text{Hence,}}\,{\text{the}}\,{\text{total}}\,{\text{time}}\,{\text{taken}} \cr & = {10 + 2} = 12\,{\text{days}} \cr} $$

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