A machine P can print one lakh books in 8 hours, machine Q can in 10 hours while machine R can print them in 12 hours...

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 ?

Answer 1

(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 * 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 (23/60 * 60/11 ) = 23/11 hours ~ 2 hours.

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M