Question:
A pipe fills a tank in 8 hours, another empties it in 12 hours. If both are opened, how long to fill?
A pipe fills a tank in 8 hours, another empties it in 12 hours. If both are opened, how long to fill?
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Use LCM to find net rate for pipes with opposing actions, or subtract rates directly.
Updated On: Jul 31, 2025
- 24 hours
- 18 hours
- 16 hours
- 20 hours
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The Correct Option is A
Solution and Explanation
- Step 1: Determine rates. Tank capacity = LCM(8, 12) = 24 units. Fill rate = $\frac{24}{8} = 3$ units/hour. Empty rate = $\frac{24}{12} = 2$ units/hour.
- Step 2: Net rate. $3 - 2 = 1$ unit/hour.
- Step 3: Time to fill. $\frac{24}{1} = 24$ hours.
- Step 4: Alternative. Fill rate = $\frac{1}{8}$ tank/hour, empty rate = $\frac{1}{12}$. Net rate = $\frac{1}{8} - \frac{1}{12} = \frac{3 - 2}{24} = \frac{1}{24}$. Time = $24$ hours.
- Step 5: Verify. Matches option (1).
- Step 6: Conclusion. Option (1) 24 hours is correct.
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