Multiple choice

Directions: Solve the following question and mark the best possible option. A tank has an inlet pipe and an outlet pipe. If the outlet pipe is closed then the inlet pipe fills the empty tank in 8 hours. If the outlet pipe is open then the inlet pipe fills the empty tank in 10 hours. If only the outlet pipe is open then in how many hours the full tank becomes half-full?

  1. 20

  2. 30

  3. 40

  4. 45
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let inlet rate be I and outlet rate be O. Given 1/I = 8, so I = 1/8. With outlet open, net rate is 1/10, so I - O = 1/10. Substituting I, 1/8 - O = 1/10, so O = 1/8 - 1/10 = 1/40. Time for outlet to empty full tank is 40 hours. Time for half-full is 40/2 = 20 hours.

AI explanation

Using the rate formula, the inlet pipe fills 1/8 of the tank per hour. When both the inlet and outlet are open, the net filling rate is 1/10 of the tank per hour. The outlet pipe's emptying rate is 1/8 minus 1/10, which equals 5/40 minus 4/40, resulting in 1/40 of the tank per hour. Therefore, it takes 40 hours for the outlet pipe to empty a full tank. To empty half of the tank, the time required is 40 divided by 2, which equals 20 hours. The answer is 20.

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