Question

Water is pouring into a tank at a constant rate when the tank is full 10 pumps of equal capacity empty the tank in 12 hours by 15 pounds of the same capacity empty the tank in 6 hours find the time in which 25 pumps of the same capacity take to empty the tank if the tank is initially full

Answer 1

Step-by-step explanation:

Given Water is pouring into a tank at a constant rate when the tank is full 10 pumps of equal capacity empty the tank in 12 hours while 15 pumps of the same capacity empty the tank in 6 hours find the time in which 25 pumps of the same capacity take to empty the tank if the tank is initially full

• Suppose the pump is being emptied it will be positive work, so let this be x in 12 hrs.
• Therefore one pump will empty in 1/x hrs.
• To fill the tank let it be y work. So to fill it will be negative, so -y.
• Therefore it will fill in -1/y hrs.
• So 1/x – 1/y = 1/12
• So 10 pumps will empty the tank
• So 10/x – 1/y = 1/12 -------------1
• Similarly for 15 pumps we get
• 15/x – 1/y = 1/6 ------------------2
• We need to find for 25/x – 1/y = ?
• So subtracting eqn 2 – 1 we get
• 5/x = 1/12, x = 60
• Consider eqn 2 we get
• -1/y = 1/6 – 15/x
• -1/y = 1/6 – 15/60
• -1/y = 1/6 – 1/4
• -1/y = - 1/12
• Therefore 25/x – 1/y
•              = 5/12 – 1/12
•             = 4/12
•            = 1/3  

So it will take 3 hrs to empty the tank.