Practice Questions
Concept Explanation
A pipe filling a tank is an inlet; a pipe emptying it is an outlet. Treat fill rate as positive and empty rate as negative.
Key Formulas
- Inlet alone fills in a days ⇒ rate = 1/a tank per day
- Outlet alone empties in b days ⇒ rate = −1/b
- Net rate with one inlet and one outlet: 1/a − 1/b
- Time to fill = 1 / Net rate
Example
Inlet fills in 12 hours, outlet empties in 18 hours. Net rate = 1/12 − 1/18 = 1/36. Tank fills in 36 hours.
Common Trap
Subtract outlet rate from inlet rate; do not add them when one pipe empties the tank.
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Q1 Medium
An inlet pipe can fill a tank in 12 hours and an outlet pipe can empty the full tank in 18 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationNet filling rate = 1/12 − 1/18 = 1/36. Time to fill = 36 hours. -
Q2 Medium
Pipe A can fill a tank in 6 hours and pipe B can empty the full tank in 8 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationNet filling rate = 1/6 − 1/8 = 1/24. Time to fill = 24 hours. -
Q3 Easy
Two inlet pipes can fill a tank separately in 10 hours and 15 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationTogether time = (10 × 15)/(10 + 15) = 6 hours. -
Q4 Easy
Inlet pipe A can fill a tank in 8 hours and inlet pipe B can fill it in 24 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationTogether time = (8 × 24)/(8 + 24) = 6 hours. -
Q5 Medium
An inlet pipe can fill a tank in 20 hours and an outlet pipe can empty the full tank in 30 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationNet filling rate = 1/20 − 1/30 = 1/60. Time to fill = 60 hours. -
Q6 Hard
Three inlet pipes can fill a tank separately in 12 hours, 15 hours and 20 hours. If all three pipes are opened together, in how many hours will the tank be filled?
ExplanationCombined rate = 1/12 + 1/15 + 1/20 = 1/5. Time to fill = 5 hours. -
Q7 Medium
An inlet pipe can fill a tank in 4 hours and an outlet pipe can empty the full tank in 12 hours. What part of the tank is filled in one hour when both pipes are open?
ExplanationNet filling rate per hour = 1/4 − 1/12 = 1/6.
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Q8 Easy
Inlet pipe A can fill a tank in 9 hours and inlet pipe B can fill it in 18 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationTogether time = (9 × 18)/(9 + 18) = 6 hours. -
Q9 Hard
An inlet pipe can fill a tank in 15 hours and an outlet pipe can empty the full tank in 20 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationNet filling rate = 1/15 − 1/20 = 1/60. Time to fill = 60 hours. -
Q10 Medium
An inlet pipe can fill a tank in 5 hours and an outlet pipe can empty the full tank in 20 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationNet filling rate = 1/5 − 1/20 = 3/20. Time to fill = 20/3 hours. -
Q11 Easy
Two inlet pipes can fill a tank separately in 4 hours and 12 hours. What part of the tank is filled in one hour when both pipes are open together?
ExplanationCombined filling rate = 1/4 + 1/12 = 1/3 per hour. -
Q12 Hard
An inlet pipe can fill a tank in 10 hours and an outlet pipe can empty the full tank in 40 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationNet filling rate = 1/10 − 1/40 = 3/40. Time to fill = 40/3 ≈ 13.33 hours. -
Q13 Hard
Inlet pipe A can fill a tank in 8 hours, inlet pipe B can also fill it in 8 hours, and an outlet pipe can empty the full tank in 24 hours. If all three pipes are opened together, in how many hours will the tank be filled?
ExplanationNet filling rate = 1/8 + 1/8 − 1/24 = 5/24. Time to fill = 24/5 = 4.8 hours. -
Q14 Medium
An outlet pipe can empty a full tank in 16 hours and an inlet pipe can fill the empty tank in 8 hours. If both pipes are opened together, in how many hours will the tank be filled?
ExplanationNet filling rate = 1/8 − 1/16 = 1/16. Time to fill = 16 hours.
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DS1 Medium
In how many hours will the tank be filled?
Statement IAn inlet pipe can fill the tank in 12 hours.
Statement IIAn outlet pipe can empty the full tank in 18 hours.
ExplanationNet filling rate is 1/36, so the tank is filled in 36 hours. -
DS2 Easy
In how many hours will the two inlet pipes fill the tank together?
Statement IInlet pipe A can fill the tank in 10 hours.
Statement IIInlet pipe B can fill the tank in 15 hours.
ExplanationBoth inlet times are needed: (10 × 15)/(10 + 15) = 6 hours.
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DS3 Medium
What is the net filling rate of the tank per hour?
Statement IAn inlet pipe can fill the tank in 6 hours.
Statement IIAn outlet pipe can empty the full tank in 8 hours.
ExplanationNet filling rate = 1/6 − 1/8 = 1/24 per hour. -
DS4 Medium
If both pipes remain open, is the tank filled within 30 hours?
Statement IAn inlet pipe can fill the tank in 20 hours.
Statement IIAn outlet pipe can empty the full tank in 30 hours.
ExplanationBoth rates are needed: net rate is 1/60, so fill time is 60 hours.