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 the work. Approximately at what time will the work be finished?
Solution
Correct Answer: Option D
Machine P’s one hour work = 1/8
Machine Q’s one hour work = 1/10
Machine R’s one hour work = 1/12
Machine (P + Q + R)’s one hour work = 1/8 + 1/10 +1/12 = (15 + 12 + 10)/120
= 37/120
For two hours (9:00 am to 11:00 am) work done by (P + Q + R) = 2 × 37/120 = 74/120
Remaining work = 1 – 74/120 = 46/120
= 23/60
(Q + R)’s one hour work = 1/10 + 1/12 = (6 + 5)/60 =11/60
Since machine P is closed at 11 a.m. and the remaining two machines complete the work
11/60 of work is completed by (Q + R) in one hour
23/60 of work will be completed by (Q + R) in (23/60 × 60/11) = 23/11 hours ≈ 2.09 hours
Thus, (Q + R) work for nearly 2 more hours to finish the work.
Therefore, approximately at 1:00 p.m. the work will be finished.
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