A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?

Solution(By Examveda Team)

$$\eqalign{ & \left( {{\text{P + Q + R}}} \right){\text{'s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} \cr & = {\frac{1}{8} + \frac{1}{{10}} + \frac{1}{{12}}} = \frac{{37}}{{120}} \cr & {\text{Work}}\,{\text{done}}\,{\text{by}}\,{\text{P,}}\,{\text{Q}}\,{\text{and}}\,{\text{R}}\,{\text{in}}\,{\text{2}}\,{\text{hours}} \cr & = {\frac{{37}}{{120}} \times 2} = \frac{{37}}{{60}} \cr & {\text{Remaining}}\,{\text{work}} = {1 - \frac{{37}}{{60}}} = \frac{{23}}{{60}} \cr & \left( {{\text{Q + R}}} \right){\text{'s}}\,{\text{1}}\,{\text{hour's}}\,{\text{work}} \cr & = {\frac{1}{{10}} + \frac{1}{{12}}} = \frac{{11}}{{60}} \cr & {\text{Now}},\frac{{11}}{{60}}\,{\text{work}}\,{\text{is}}\,{\text{done}}\,{\text{by}}\,{\text{Q}}\,\,{\text{and}}\,{\text{R}}\,{\text{in}}\,{\text{1}}\,{\text{hour}} \cr & {\text{So}},\frac{{23}}{{60}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{done}}\,{\text{by}}\,{\text{Q}}\,{\text{and}}\,{\text{R}}\,{\text{in}} \cr & = {\frac{{60}}{{11}} \times \frac{{23}}{{60}}} = \frac{{23}}{{11}}\,{\text{hours}} \approx 2\,{\text{hours}} \cr & {\text{So,}}{\text{the}}\,{\text{work}}\,{\text{will}}\,{\text{be}}\,{\text{finished}}\,{\text{approximately}} \cr & {\text{2}}\,{\text{hours}}\,{\text{after}}\,{\text{11}}\,{\text{A}}{\text{.M}}{\text{.,}}\,{\text{i}}{\text{.e}}{\text{.,}}\,{\text{around}}\,{\text{1}}\,{\text{P}}{\text{.M}}{\text{.}} \cr} $$