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Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining par in 7 hours. The number of hours taken by C alone to fill the tank is?

Correct answer: C. 14

  • A. 10
  • B. 12
  • C. 14
  • D. 16

Explanation

Together, A, B and C fill 1/6 tank per hour, so in 2 hours they fill 1/3 and leave 2/3. A and B fill that remaining 2/3 in 7 hours, giving their rate 2/21 tank per hour; hence C's rate is 1/6 - 2/21 = 1/14 tank per hour, so C alone takes 14 hours. The likely mistake is choosing 12 hours by treating C's time as the combined time or failing to subtract A and B's rate.

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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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