Subject: General Aptitude · Chapter: Time and Work · Exam: · Marks: · Difficulty:
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)11 : 30 a.m.
(b)12 noon
(c)12 : 30 p.m.
(d)1 p.m.
Answer
Answer (as printed): D
Explanation
(P+Q+R)'s 1 hour's work $=\left(\frac{1}{8}+\frac{1}{10}+\frac{1}{12}\right)=\frac{37}{120}$. Work done by P, Q and R in 2 hours $=\left(\frac{37}{120} \times 2\right)=\frac{37}{60}$. Remaining work $=\left(1-\frac{37}{60}\right)=\frac{23}{60}$. (Q+R)'s 1 hour's work $=\left(\frac{1}{10}+\frac{1}{12}\right)=\frac{11}{60}$. 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 $\left(\frac{23}{60} \times \frac{60}{11}\right)=\frac{23}{11} \approx 2$ hours. So, the work will be finished approximately 2 hours after 11 a.m., i.e., around 1 p.m.
Explanation as extracted from the printed page; notation may be imperfect.