Fraction of Tank Filled by Pipes with Solved Examples
Fraction of Tank Filled problems use the rate at which a pipe fills or empties a tank. If a pipe fills a tank in T hours, its rate is 1/T tank per hour, so the fraction filled in t hours is t/T. For multiple pipes, add inlet rates and subtract outlet rates.
On this page
What Is the Fraction of Tank Filled?
A pipe that fills a tank in T hours fills 1/T of the tank in one hour. Therefore, in t hours it fills t × 1/T = t/T. The fraction cannot exceed 1 unless the calculation represents repeated filling or overflow. For an empty tank, the fraction remaining is 1 − t/T.
Fraction of Tank Filled Video Lessons
Watch short topic-wise lessons for quick revision.
Pipes and Leaks: Tank Filling Fractions
Understand how leaks affect pipe efficiency and calculate the fraction of a tank filled or emptied using time-and-work methods.
Fraction of Tank Filled Formula & Tricks
Important Formulas
Here, T is the time taken to fill the whole tank and t is the operating time.
A pipe completing one full tank in T hours fills 1/T of the tank in one hour.
Add the rates of all pipes that fill the tank.
Subtract the emptying rate from the filling rate when both pipes operate simultaneously.
For example, filling 3/5 of a tank with a pipe that takes T hours requires 3T/5 hours.
This applies when the initial tank is empty and no water is removed during filling.
Quick Tricks
For one pipe, divide the operating time by the full filling time instead of calculating the hourly rate separately.
For several pipes, assume the tank capacity equal to the LCM of their filling times. Convert each pipe into units filled per hour.
An outlet reduces the filled fraction, so its rate must be subtracted. If the outlet rate is greater, the net rate is negative and the tank empties.
Fraction of Tank Filled Concepts
Fraction Filled by One Pipe
The full tank is represented by 1. Since the pipe fills 1/T in one hour, multiplying by t gives t/T. Reduce the fraction to its lowest terms where possible.
Fraction Filled by Two or More Inlet Pipes
If pipes take T₁ and T₂ hours, their combined rate is 1/T₁ + 1/T₂. The fraction filled in t hours is t(1/T₁ + 1/T₂), provided the tank does not overflow.
Inlet Pipe and Outlet Pipe
If the inlet fills the tank in Tinlet hours and the outlet empties it in Toutlet hours, the net rate is 1/Tinlet − 1/Toutlet. The fraction changed after t hours is t times this net rate.
Finding Full Time from a Given Fraction
Since f = t/T, rearranging gives T = t/f. This method is also useful when the question gives the filled fraction and asks for the time needed to fill the whole tank.
Remaining Fraction and Initial Water
If the initial fraction is f₀ and the net filling rate is r for t hours, the final fraction is f₀ + rt. The remaining fraction is 1 − (f₀ + rt), as long as the value lies between 0 and 1.
Fraction of Tank Filled Data Table
Use the structured data below while following the explanation and examples.
Pipe Operations and Rate Signs
The sign of each pipe rate depends on whether it adds or removes water.
| Operation | Rate contribution | Fraction after t hours |
|---|---|---|
| One inlet filling in T hours | +1/T | t/T |
| Two inlets filling in T₁ and T₂ hours | +1/T₁ + 1/T₂ | t(1/T₁ + 1/T₂) |
| One inlet and one outlet | +1/Tinlet − 1/Toutlet | t(1/Tinlet − 1/Toutlet) |
| Only an outlet emptying in T hours | −1/T | −t/T |
Note: The expressions show the change in the tank fraction from an empty starting point. Add the initial fraction separately when the tank is not empty.
Learn more concepts on PrepShots
Start ₹1 Trial →Practice Fraction of Tank Filled Questions
Practise published questions related to this topic.
Want more practice questions?
Practice in App →Fraction of Tank Filled Quick Quiz
Attempt 5 questions and check your score instantly.
Keep practising
Practice more Fraction of Tank Filled questions in the PrepShots app and continue from your current topic.
Practice More Questions - Start ₹1 Trial →Quick Revision Notes
Fraction of Tank Filled: Revision Points
Use these formulas and rules for quick calculations.
- A pipe filling a tank in T hours has rate 1/T tank per hour.
- Fraction filled by one pipe in t hours is t/T.
- Add rates of inlet pipes and subtract rates of outlet pipes.
- For an inlet and outlet, net rate = 1/Tinlet − 1/Toutlet.
- Time required for fraction f is fT for a pipe with full time T.
- If fraction f is filled in t hours, full filling time is t/f hours.
- Remaining fraction = 1 − filled fraction when the tank starts empty.
- If the net rate is negative, the tank is emptying rather than filling.
Fraction of Tank Filled FAQs
What is the fraction of tank filled formula for one pipe?
If a pipe fills the whole tank in T hours, the fraction filled in t hours is t/T. For example, a 15-hour pipe fills 4/15 of the tank in 4 hours.
How do you find the fraction filled by two pipes working together?
Add their rates and multiply by time: Fraction = t(1/T₁ + 1/T₂). Pipes taking 12 and 18 hours fill at 5/36 tank per hour together.
How is an outlet treated in fraction of tank filled problems?
Subtract the outlet rate from the inlet rate. If an inlet fills in 6 hours and an outlet empties in 9 hours, the net rate is 1/6 − 1/9 = 1/18 tank per hour.
A pipe fills 3/5 of a tank in 12 hours. How long will it take to fill the whole tank?
Full time = 12 ÷ (3/5) = 20 hours.
What fraction remains after a pipe fills 7/12 of an empty tank?
Remaining fraction = 1 − 7/12 = 5/12.
What happens if the outlet rate is greater than the inlet rate?
The net rate is negative, so the tank loses water. For example, 1/10 − 1/6 = −1/15 tank per hour.