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?

• A. $11:30$ A.M.
• B. $12$ noon
• C. $12:30$ P.M.
• D. $1:00$ P/M/

Answer 1

The correct option is D $1:00$ P/M/

$(P+Q+R)$'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 $=(\frac{37}{120}\times 2)=\frac{37}{60}$
$(Q+R)$'s $1$ hour's work$=(\frac{1}{10}+\frac{1}{12})=\frac{11}{60}$.
Now, $\frac{11}{60}$ work done 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.