A pipe can fill a cistern in 12 hours, and another pipe can empty it in 20 hours. If both pipes are opened simultaneously in an empty cistern, how long will it take to fill it completely?

Question

Accepted Answer

This is a standard work and time problem involving inlets and outlets (pipes and cisterns).

### Step-by-Step Solution:
1. **Work done by inlet pipe in 1 hour:** $\frac{1}{12}$
2. **Work done by outlet pipe in 1 hour:** $-\frac{1}{20}$ (negative because it empties)
3. **Net work done in 1 hour when both are open:**
   $$	ext{Net 1-hour work} = \frac{1}{12} - \frac{1}{20}$$
   Find the LCM of 12 and 20, which is 60:
   $$	ext{Net 1-hour work} = \frac{5 - 3}{60} = \frac{2}{60} = \frac{1}{30}$$
4. **Total time to fill the cistern:**
   $$	ext{Total Time} = \frac{1}{	ext{Net 1-hour work}} = 30 	ext{ hours}$|

**Answer:** It will take **30 hours** to fill the cistern.

A pipe can fill a cistern in 12 hours, and another pipe can empty it in 20 hours. If both pipes are opened simultaneously in an empty cistern, how long will it take to fill it completely? - DDCET Q&A

A pipe can fill a cistern in 12 hours, and another pipe can empty it in 20 hours. If both pipes are opened simultaneously in an empty cistern, how long will it take to fill it completely?

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