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CAT 2023 Slot 2 · Quant · Time and Work · medium

Pipe A can fill a tank in 15 hours and pipe B can fill it in 20 hours. An outlet pipe C can empty the full tank in 30 hours. If all three pipes are…

Single correct option

Pipe A can fill a tank in 15 hours and pipe B can fill it in 20 hours. An outlet pipe C can empty the full tank in 30 hours. If all three pipes are opened together, in how many hours will the tank be filled?
  1. A. 10 hours
  2. B. 12 hours
  3. C. 14 hours
  4. D. 16 hours
Show answer and solution

Answer: (B) 12 hours

Rate of A = 1/15, rate of B = 1/20 (filling), rate of C = 1/30 (emptying). Combined rate = 1/15 + 1/20 − 1/30. Taking LCM 60: 4/60 + 3/60 − 2/60 = 5/60 = 1/12 of the tank per hour. So the tank fills in 12 hours.
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Original question written in the CAT 2023 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake