Question

A pipe can fill a cistern in 12 hours, while another pipe can empty it in 18 hours. If both the pipes are opened simultaneously, in how many hours the cistern will be filled?

• A. 24 hours
• B. 36 hours
• C. 30 hours
• D. 27 hours

Hint:

Net time $= \frac{xy}{y - x} = \frac{12 \times 18}{18 - 12} = \frac{216}{6} = 36$ hours.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Net filling rate is the filling rate minus the emptying rate.

Step 2: Key Formula or Approach:
1. Filling rate of pipe A: $\frac{1}{12}$ cistern/hour.
2. Emptying rate of pipe B: $\frac{1}{18}$ cistern/hour.
Net rate when both pipes operate simultaneously:
\[\text{Net Rate} = \frac{1}{12} - \frac{1}{18} = \frac{3 - 2}{36} = \frac{1}{36}\text{ cistern/hour}\]

Step 3: Detailed Explanation:
Total time required to fill the cistern:
\[\text{Time} = \frac{1}{\text{Net Rate}} = 36\,\text{hours}\]

Step 4: Final Answer:
Thus, the cistern will be filled in 36 hours.