Question

A machine P can print one laakh 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. 11 : 30 a.m
• B. 12 noon
• C. 12 : 30 p.m
• D. 1 p.m

Answer 1

The correct option is D 1 p.m

(P + Q + R)'s 1 hours' work = $(\frac{1}{8}+\frac{1}{10}+\frac{1}{12})=\frac{37}{120}$
$\therefore$ Work done by (P + Q + R) in 2 hours = 2 $\times \frac{37}{120}=\frac{37}{60}$
Remaining work = $(1-\frac{37}{60})=\frac{23}{60}$ (Q + R)'s 1 hours' work = $(\frac{1}{10}+\frac{1}{12})=\frac{11}{60}$
$\frac{11}{60}$ of the work is done by (Q + R) in 1 hour $\therefore$ $\frac{23}{60}$ of the work will bw done by (Q + R)
in $\frac{23}{60}÷\frac{11}{60}=\frac{23}{11}=2\frac{1}{11}$ hours $\simeq$ 2 hours So the work will be finished
approximately 2 hours after 11 a.m., i.e, around 1 p.m