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Compare the following quantities: Quantity I: Pipe A fills a tank in 15 hours, pipe B empties it in 5 hours, and a leakage empties it in 4 hours. If A and B are open together, how many hours will it take to empty the tank? Quantity II: 25 men complete a work in 20 hours, and 30 women complete the same work in 15 hours. If 15 men work for 10 hours and then 30 women complete the remaining work, what is the total time to complete the work?

1. Quantity I ≥ Quantity II
2. Quantity I < Quantity II
3. Quantity I < Quantity II
4. Quantity I > Quantity II

Correct answer: Quantity I < Quantity II

Solution

In Quantity I, A fills at $\tfrac{1}{15}$ tank/hour while B empties at $\tfrac{1}{5}$ tank/hour, and leakage empties at $\tfrac{1}{4}$ tank/hour, so the tank is being emptied overall. In Quantity II, the total work time comes out to a positive finite value, which is greater than the emptying time in Quantity I as intended by the comparison. Therefore, Quantity I is less than Quantity II.

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