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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 started at 9 a.m while machine P 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.mB. 12 noonC. 12:30 p.mD. 1 p.m

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 started at 9 a.m while machine P 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.mB. 12 noonC. 12:30 p.mD. 1 p.m

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
11 months ago
Let's calculate the work done by machine P in 2 hours (from 9 a.m to 11 a.m): Machine P can print 1 lakh books in 8 hours, so in 1 hour it can print 1/8th of the books. Therefore, in 2 hours, it can print 1/8 * 2 = 1/4th of the books. So, machine P printed 1/4th of 1 lakh books, which is 25,000 books, in 2 hours. Now, let's calculate the work done by machines Q and R in 1 hour: Machine Q can print 1 lakh books in 10 hours, so in 1 hour it can print 1/10th of the books. Similarly, machine R can print 1/12th of the books in 1 hour. So, in 1 hour, machines Q and R together can print 1/10 + 1/12 = 11/60th of the books. After machine P closed at 11 a.m, the remaining work is to print 3/4th of 1 lakh books, which is 75,000 books. At the rate of 11/60th of the books printed per hour, machines Q and R can print 75,000 books in (75,000 / (11/60)) hours, which is approximately 4091.67 hours. Adding this time to the time when machine P closed at 11 a.m, we get: 11 a.m + 4091.67 hours = 12:30 p.m (approximately) Therefore, the work will be finished approximately at 12:30 p.m. So, the answer is (C) 12:30 p.m.

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