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A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

Correct answer: B. 3 hrs 45 min

  • A. 3 hrs 15 min
  • B. 3 hrs 45 min
  • C. 4 hrs
  • D. 4 hrs 15 min

Explanation

The first tap fills half the tank in 6/2 = 3 hours. Three more similar taps make four taps, whose combined rate is 4/6 = 2/3 tank per hour, so the remaining half takes (1/2)/(2/3) = 3/4 hour = 45 minutes. The total time is 3 hours 45 minutes, and the likely mistake is choosing 4 hours by treating the extra taps as if they were opened from the start.

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About Time and Work

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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