Multiple choice

Three pipes P , Q , R can separately fill a cistern in 4 , 8 and 12 hours respectively. Another pipe S can empty the completely filled cistern in 10 hours. Which of the following arrangements will fill the empty cistern in less time than others?

  1. Q alone

  2. P and S are open

  3. P, R and S are open

  4. P, Q and S are open
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rates: P = 1/4, Q = 1/8, R = 1/12 (fill), S = -1/10 (empty). Option A: Q alone = 1/8, time = 8 hours. Option B: P + S = 1/4 - 1/10 = 3/20, time = 20/3 = 6.67 hours. Option C: P + R + S = 1/4 + 1/12 - 1/10 = 1/5, time = 5 hours. Option D: P + Q + S = 1/4 + 1/8 - 1/10 = 9/40, time = 40/9 = 4.44 hours. Option D is fastest.

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