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 the work. Approximately at what time will the work be finished?

• A. 12 noon
• B. 12:30 p.m.
• C. 1 p.m.
• D. 11 p.m.

Answer 1

The correct option is C

1 p.m.

P`s 1 hour`s work = $\frac{1}{8}$
Q`s 1 hour`s work = $\frac{1}{10}$
R`s 1 hour`s work = $\frac{1}{12}$

(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 $=(\frac{37}{120}\times 2)=\frac{37}{60}$

Remaining work $=(1-\frac{37}{60})=\frac{60-37}{60}=\frac{23}{60}$

(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 $\frac{60}{11}\times \frac{23}{60}=\frac{23}{11}hours\approx 2hours.$

So, the work will be finished approximately 2 hours after 11 a.m., i.e. at around 1 p.m.