Multiple choice

An empty tank is connected with pipes A, B and C. A and B inlet pipes and they fill the tank in $6$ hours and $8$ hours respectively. While C is an outlet pipe and it empties the completely filled tank in $5$ hours. Find the time in which the tank will be completely filled if all the pipes are opened together.

  1. $\dfrac{119}{11}$ hours
  2. $\dfrac{108}{11}$ hours
  3. $\dfrac{120}{11}$ hours
  4. $\dfrac{109}{11}$ hours
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C Correct answer
Explanation

Rates: A = 1/6, B = 1/8, C = -1/5. Combined rate = 1/6 + 1/8 - 1/5 = (20 + 15 - 24) / 120 = 11/120. Time = 120/11 hours.

AI explanation

Using the net work formula, the combined rate of pipes A, B, and C is 1/6 + 1/8 - 1/5. Finding a common denominator of 120 gives 20/120 + 15/120 - 24/120 = 11/120 of the tank per hour. The total time to fill the tank is the reciprocal of this combined rate, which is 120/11 hours.

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