Time and Work - Arithmetic Aptitude Questions and Answers

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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 ?

11:30 A.M.

12 noon

12:30 P.M.

1:00 P.M.

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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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