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### Discussion :: Time and Work

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 ?
2.  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 =[$$\frac { 1 } {8 }$$+$$\frac { 1 } {10 }$$+$$\frac { 1 } {12 } ]$$=$$\frac { 37 } {120}$$

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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