Discussion :: Time and Work

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
Explanation :
(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 =[\(\frac { 37 } {120} \)*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[\(\frac { 60 } { 11 }\)\( *\frac { 23 } {60 } \)]=\(\frac { 23 } {11} \)hours 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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