Practice Questions
Concept Explanation
A leak behaves like an outlet pipe. When a tap fills the tank while a leak drains it, use net rate = fill rate − leak rate.
Key Formulas
- Tap fills in a hours, leak empties in b hours ⇒ net = 1/a − 1/b
- Effective fill time = 1 / (1/a − 1/b)
- If net rate is negative, the tank never fills with only the tap open
Example
Tap fills in 10 hours, leak empties in 15 hours. Net = 1/10 − 1/15 = 1/30. Effective fill time = 30 hours.
Common Trap
A leak slows filling; effective time is longer than the tap-alone time, not shorter.
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Q1 Hard
A tap can fill a tank in 10 hours, but because of a leak it takes 15 hours to fill the tank. In how many hours can the leak alone empty a full tank?
Explanation1/10 − 1/L = 1/15. So 1/L = 1/30 and the leak alone empties the tank in 30 hours. -
Q2 Medium
A tap can fill a tank in 12 hours and a leak can empty the full tank in 24 hours. If the tap is opened and the leak is also working, in how many hours will the tank be filled?
ExplanationEffective filling rate = 1/12 − 1/24 = 1/24. Time to fill = 24 hours. -
Q3 Easy
A tap can fill a tank in 8 hours and a leak can empty the full tank in 40 hours. If both are working together, in how many hours will the tank be filled?
ExplanationEffective filling rate = 1/8 − 1/40 = 1/10. Time to fill = 10 hours. -
Q4 Easy
A tap can fill a tank in 6 hours and a leak can empty the full tank in 12 hours. What is the effective time taken to fill the tank when both are working?
ExplanationEffective filling rate = 1/6 − 1/12 = 1/12. Time to fill = 12 hours. -
Q5 Medium
A tap can fill a tank in 20 hours and a leak can empty the full tank in 30 hours. If both are working together, in how many hours will the tank be filled?
ExplanationEffective filling rate = 1/20 − 1/30 = 1/60. Time to fill = 60 hours. -
Q6 Hard
A tap can fill a tank in 15 hours and a leak can empty the full tank in 20 hours. What is the effective time taken to fill the tank when both are working?
ExplanationEffective filling rate = 1/15 − 1/20 = 1/60. Time to fill = 60 hours. -
Q7 Hard
A tap alone can fill a tank in 9 hours, but with a leak open it takes 18 hours to fill the tank. In how many hours can the leak alone empty a full tank?
Explanation1/9 − 1/L = 1/18. So the leak alone empties the tank in 18 hours.
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Q8 Easy
A tap can fill a tank in 4 hours and a leak can empty the full tank in 8 hours. What part of the tank is filled in one hour when both are working?
ExplanationEffective filling rate = 1/4 − 1/8 = 1/8 per hour. -
Q9 Medium
A tap can fill a tank in 30 hours and a leak can empty the full tank in 60 hours. What is the effective time taken to fill the tank when both are working?
ExplanationEffective filling rate = 1/30 − 1/60 = 1/60. Time to fill = 60 hours. -
Q10 Medium
A tap can fill a tank in 5 hours and a leak can empty the full tank in 20 hours. In how many hours will the tank be filled when both are working?
ExplanationEffective filling rate = 1/5 − 1/20 = 3/20. Time to fill = 20/3 hours. -
Q11 Easy
A tap can fill a tank in 24 hours and a leak can empty the full tank in 48 hours. What is the effective time taken to fill the tank when both are working?
ExplanationEffective filling rate = 1/24 − 1/48 = 1/48. Time to fill = 48 hours. -
Q12 Medium
A tap can fill a tank in 10 hours and a leak can empty the full tank in 15 hours. If both are working together, in how many hours will the tank be filled?
ExplanationEffective filling rate = 1/10 − 1/15 = 1/30. Time to fill = 30 hours. -
Q13 Medium
A tap can fill a tank in 7 hours and a leak can empty the full tank in 21 hours. What is the effective time taken to fill the tank when both are working?
ExplanationEffective filling rate = 1/7 − 1/21 = 2/21. Time to fill = 21/2 = 10.5 hours. -
Q14 Easy
A tap can fill a tank in 16 hours and a leak can empty the full tank in 32 hours. In how many hours will the tank be filled when both are working?
ExplanationEffective filling rate = 1/16 − 1/32 = 1/32. Time to fill = 32 hours.
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DS1 Medium
What is the effective time taken to fill the tank?
Statement IA tap can fill the tank in 10 hours.
Statement IIA leak can empty the full tank in 15 hours.
ExplanationEffective filling rate is 1/30, so the tank is filled in 30 hours. -
DS2 Hard
In how many hours can the leak alone empty a full tank?
Statement IThe tap alone can fill the tank in 9 hours.
Statement IIWith the leak open, the tank is filled in 18 hours.
Explanation1/9 − 1/L = 1/18, so the leak alone takes 18 hours.
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DS3 Easy
What is the effective filling rate of the tank per hour?
Statement IThe tap can fill the tank in 6 hours.
Statement IIThe leak can empty the full tank in 12 hours.
ExplanationBoth rates are needed: effective rate = 1/6 − 1/12 = 1/12 per hour. -
DS4 Medium
Is the effective fill time less than 12 hours?
Statement IThe tap can fill the tank in 8 hours.
Statement IIThe leak can empty the full tank in 40 hours.
ExplanationTogether: effective rate is 1/10, so fill time is 10 hours.