Question

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?

• A. 40
• B. 35
• C. 20
• D. 30
• E. 25

Hint:

In pipe and tank problems, always express rates as work per unit time. The net rate is the sum of filling rates (positiv(e) minus emptying rates (negativ(e).

Answer 1

The Correct Option is C

Step 1: Define Work Rates:
Let the tank's capacity be 1 unit. Inlet pipe fills rate: $I = \frac{1}{8}$ tank per hour. With outlet open, net fill rate = $\frac{1}{10}$ tank per hour.
Step 2: Find Outlet Rate:
Net rate = Inlet rate - Outlet rate. $\frac{1}{10} = \frac{1}{8} - O$, where $O$ is the outlet's emptying rate. $O = \frac{1}{8} - \frac{1}{10} = \frac{5-4}{40} = \frac{1}{40}$ tank per hour.
Step 3: Time to Empty Half the Tank:
To empty half the tank ($\frac{1}{2}$ unit) at rate $\frac{1}{40}$ per hour: Time = $\frac{\text{Work}}{\text{Rate}} = \frac{1/2}{1/40} = \frac{1}{2} \times 40 = 20$ hours.
Step 4: Final Answer:
It will take 20 hours for the full tank to become half-full with only the outlet pipe open.