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1. 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.

Solution:

\begin{aligned} (P + Q + R)'s 1 hour's work \\ = \frac{1}{8} + \frac{1}{10} + \frac{1}{12} = \frac{37}{120} \\ Work done by P, Q and R in 2 hours \\ = \frac{37}{120} \times 2 = \frac{37}{60} \\ Remaining work = 1 - \frac{37}{60} = \frac{23}{60} \\ (Q + R)'s 1 hour's work \\ = \frac{1}{10} + \frac{1}{12} = \frac{11}{60} \\ Now, \frac{11}{60} work is done by Q and R in 1 hour \\ So, \frac{23}{60} work will be done by Q and R in \\ = \frac{60}{11} \times \frac{23}{60} = \frac{23}{11} hours \approx 2 hours \\ So, the work will be finished approximately \\ 2 hours after 11 A .M ., i .e ., around 1 P .M . \end{aligned}

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