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 ?

(a) 11:30 A.M.

(b) 12 noon

(c) 12:30 P.M.

(d) 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 x 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 x 23/60) = 23/11 = 2 hours