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?

Question: 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:(P + Q + R)'s 1 hour's work = (1/8 + 1/10 + 1/12) = 37/120Work done by P, Q and R in 2 hours = (37/120) × 2 = 37/60Remaining work = (1 - 37/60) = 23/60(Q + R)'s 1 hour's work = (1/10 + 1/12) = 11/60Now,11/60 of the work is done by Q and R in 1 hour.23/60 of work will be done by Q and R in (60/11) × (23/60) = 23/11 hours = 2.09 hours ≈ 2 hoursSo, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.