Two pipes are connected to tank 1 and one pipe connects tank 1 and tank 2 at the bottom of both tanks. At first pipe A and pipe B will filling tank 1 and then pipe C would be opened to fill tank 2. Capacity of tank 1 is twice capacity of tank 2. Pipe C takes 8 minutes to fill the whole tank 2 wherein discharging capacity of pipe C is 62.5 liters per minute. Ratio of time taken by pipe A and B to fill the tank when operating alone is 4 : 5 then find approximate discharging capacity of pipe A and B in liters/ minute if both the pipes discharge equal amount of water in tank. Time taken by pipe A and B to fill the tank 1 is 20/ 3 minutes?

Option 2 : 42 liters/minute, 33 liters/ minute

Given:

Pipe A and B = Tank 1

Pipe C = Tank 2

Discharging capacity of pipe C = 62.5 liters/ minute

Time taken to fill the whole tank 2 = 8 minutes

Pipe A:  pipe B = 4: 5 (Time taken to fill the tank)

Time taken to fill tank 1 = 20/ 3 minutes

Formula:

If time taken by pipe A to fill tank is ‘a’ minutes and by pipe B is ‘b’ minutes then total time taken to fill the tank t ⇒ (1/ t)= (1/ a) + (1/ b)

If time taken by pipe A to fill tank is ‘a’ minutes and by pipe B is ‘b’ minutes to empty the tank then total time taken to fill the tank t ⇒ (1/ t)= (1/ a) - (1/ b)

Calculation:

Capacity of tank 2 = 62.5 × 8

⇒ Capacity of tank 2 = 500 liters

⇒ Capacity of tank 1 = 1000 liters (∵ 500 × 2 = 1000)

Let, time taken by pipe A to fill the tank be X

⇒ time taken by pipe B = 5X/ 4

⇒ 3/ 20 = (1/ X) + (4/ 5X)

⇒ 3/ 20 = 9/ 5X

⇒ 5X = 60

⇒ X = 12 minutes

⇒ Time taken by pipe B to fill the tank = 15 minutes

⇒ Discharge capacity of pipe A = 500/ 12

⇒ Discharge capacity of pipe A ≈ 42 liters/ minute (∵ 500/12 = 41.66)

⇒ Discharge capacity of pipe B = 500/ 15

⇒ Discharge capacity if pipe B = 33.33 liters/ minute

∴ discharging capacity of pipe A and B is approximately 42 liters/ minute and 33 liters/ minute respectively