Three pipes can fill the tank in 12 hours. One of the pipes can fill it in 10…
2025
Three pipes can fill the tank in 12 hours. One of the pipes can fill it in 10 hrs and the other pipe can empty in 15 hours. At what rate does the third pipe work ?
- A.
Waste pipe emptying the tank in 20 hours
- B.
Filling the tank in 10 hours.
- C.
Filling the tank in 20 hours.
- D.
Waste pipe emptying the tank in 10 hours.
Attempted by 12 students.
Show answer & explanation
Correct answer: C
Key idea: work with rates (fraction of tank per hour).
First pipe fills at a rate of 1/10 tank per hour.
Second pipe empties at a rate of 1/15 tank per hour, so its contribution is -1/15.
Let the third pipe's rate be 1/x (positive means filling). The combined rate is given as 1/12.
Set up the equation: 1/10 - 1/15 + 1/x = 1/12.
Solve for 1/x: 1/x = 1/12 - 1/10 + 1/15.
Compute the right-hand side: 1/12 - 1/10 = (5 - 6)/60 = -1/60; then -1/60 + 1/15 = -1/60 + 4/60 = 3/60 = 1/20.
Thus 1/x = 1/20, so x = 20.
Answer: The third pipe fills the tank in 20 hours.