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: Option D
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(P + Q + R)'s 1 hour's work = \(\left(\frac{1}{8}+\frac{1}{10}+\frac{1}{12}\right) = \frac{37}{120}\)
Work done by P, Q and R in 2 hours = \(\left(\frac{37}{120}\times2\right) = \frac{37}{60}\)
Remaining work = \(\left(1-\frac{37}{60}\right) = \frac{23}{60}\)
(Q + R)'s 1 hour's work = \( \left(\frac{1}{10}+\frac{1}{12}\right)=\frac{11}{60}\)
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 \(\left(\frac{60}{11}\times \frac{23}{60}\right) = \frac{23}{11}
\) hours appx. 2 hours.
So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.
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