Tap A fills a tank in 25 minutes, Tap B fills it in 40 minutes, and Tap C empties it in 30 minutes. If all three taps are opened together on an empty tank, will the tank be filled or emptied, and in how many minutes?
Correct Answer: None of these
Introduction / Context:Sum the two inlet rates and subtract the outlet rate. If the net is positive, the tank fills; if negative, it empties. The magnitude of the net rate yields the time for a full tank (if filling) from empty.
Given Data / Assumptions:
- A = 1/25 tank/min.
- B = 1/40 tank/min.
- C = −1/30 tank/min.
Concept / Approach:Net rate r = 1/25 + 1/40 − 1/30. If r > 0, time to fill = 1/r minutes.
Step-by-Step Solution:
LCM 600 ⇒ r = (24 + 15 − 20)/600 = 19/600 tank/min.Since r > 0, the tank fills. Time = 1 / (19/600) = 600/19 ≈ 31.58 minutes.Verification / Alternative check:31.58 min * 19/600 ≈ 1 tank, confirming.
Why Other Options Are Wrong:Given numeric options do not match 600/19 minutes; therefore “None of these.”
Common Pitfalls:Arithmetic with mixed denominators or assuming integer results. The exact fraction 600/19 is correct.
Final Answer:None of these (net fill time = 600/19 minutes ≈ 31.58 min)