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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?
Options
11:30 A.M.
12 noon
12:30 P.M.
1:00 P.M.
Solution
1:00 P.M.
Explanation:
(P + Q + R)’s 1 hour's work = `(1/8 + 1/10 + 1/12) = 37/120`
Work done by P, Q and R in 2 hours = `(37/120 xx 2) = 37/60`
Remaining work = `(1 - 37/60) = 23/60`
(Q + R)’s 1 hour’s work = `(1/10 + 1/12) = 11/60`
Now, `11/60` work is done by Q and R in 1 hour.
So, `23/60` work will be done by Q and R in `(60/11 xx 23/60) = 23/11` hours ≈ 2 hours.
So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.