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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 the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?

Correct answer: C. 1:00 pm

  • A. 3 pm
  • B. 2 pm
  • C. 1:00 pm
  • D. 11 am

Explanation

In the first 2 hours, the three machines print 2 x (1/8 + 1/10 + 1/12) = 2 x 37/120 = 37/60 of the job. The remaining 23/60 is printed by Q and R at 1/10 + 1/12 = 11/60 job per hour, taking (23/60) ÷ (11/60 per hour) = 23/11 hours, about 2 hours 5 minutes; starting at 11:00 am, completion is about 1:05 pm, approximately 1:00 pm. Students may choose 2:00 pm by rounding the remaining time up to 3 hours.

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Problems measure work through rates, treating each person's or machine's contribution as work completed per unit time. Questions cover combined work, efficiency, wages, alternate working schedules, pipes and cisterns, and men-days relationships, with care needed to distinguish time taken by one worker from the time required when workers act together.

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