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: Understanding the Concept:
Determine individual rates of the inlet and outlet pipes. The combined rate is the difference.
Step 2: Key Formula or Approach:
Combined Rate \( = \) Inlet Rate \( - \) Outlet Rate.
Step 3: Detailed Explanation:
Inlet rate \( = 1/8 \) per hour.
Net rate \( = 1/10 \) per hour.
Outlet rate \( = 1/8 - 1/10 = (5-4)/40 = 1/40 \).
So, the outlet pipe empties the full tank in 40 hours.
To make the tank half-full, it must empty \( 1/2 \) of the tank.
Time \( = (1/2) \cdot 40 = 20 \) hours.
Step 4: Final Answer:
The time taken is 20 hours.