Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?
  • a)
    2 hours
  • b)
    1 hour 45 minutes
  • c)
    2 hour 11 minutes
  • d)
    2 hour 10 minutes
Correct answer is option 'A'. Can you explain this answer?
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SSC Question

By SOURAV KUMAR · Jun 26, 2020 ·SSC
Knowledge Hub answered Jun 26, 2020
Let the total amount of work in filling a cistern be 24 units. (LCM of 3, 4 and 8)
⇒ Work done by pipe 1 in 1 hour = 24/3 = 8 units.
⇒ Work done by pipe 2 in 1 hour = 24/4 = 6 units.
⇒ Work done by pipe 3 in 1 hour = 24/ (-8) = -3 units
⇒ Total work done in 1 hour = 8 + 6 – 3 = 11 units
∴ Time required to complete 11/12th of the work = 11/12 × 24/ 11 = 2 hours

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