A cistern can be filled by an inlet pipe in 20 hours and can be emptied by an outlet pipe in 25 hours. Both the pipes are opened. After 10 hours, the outlet pipe is closed, the total time to fill the tank is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 28 hours
In one hour the inlet fills 1/20 of the cistern and the outlet empties 1/25. With both open, the net filling per hour is
\( \displaystyle \frac{1}{20}-\frac{1}{25} = \frac{5-4}{100} = \frac{1}{100} \)
In 10 hours:
\( \displaystyle 10\times\frac{1}{100} = \frac{1}{10} \text{ of the cistern} \)
The remaining 9/10 is filled by the inlet alone:
\( \displaystyle \frac{9}{10}\div\frac{1}{20} = 18 \text{ hours} \)
Total time = 10 + 18 = 28 hours.
CBSE Applied Mathematics (Class XII):
Pipes and Cisterns
