A Time taken by pipe P and Q to fill the tank is 120/23 minutes. Time taken by drain pipe S to empty the tank is 12 minutes more than pipe P to fill the tank. Time taken by pipe Q is 15 minutes. Ratio of time taken by R to fill up the tank and by pipe Q is 4 : 5. What is total time taken to fill the whole tank when all the pipes are open ?

Option 2 : 40/9 minutes

Given:

Pipe P + Pipe Q = 120/23 minutes

Pipe S = Pipe P + 12 minutes

Pipe R: Pipe Q = 4 : 5

Pipe Q = 15 minutes

Formula:

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)

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)

Calculation:

Let, time taken by pipe P = X

⇒ 23/ 120 = (1/ X) + (1/15)

⇒ 23/ 120 = 15 + X/(15X)

⇒ 345X = 1800 + 120X

⇒ 225X = 1800

⇒ X = 8 minutes

⇒ Time taken by pipe S to drain the water = 20 minutes

⇒ Pipe R: Pipe Q = 4 : 5

Let, time taken by pipe R be Y

⇒ Y : 15 = 4 : 5

⇒ Y = 15 × 4/ 5

⇒ Y = 12 minutes

Now, placing all the values in formula

⇒ 1/ t = (1/8) + (1/15) + (1/12) – (1/20)

⇒ 1/ t = (15 + 8 + 10 – 6)/120

⇒ 1/ t = 27/120

∴ Time taken is 40/ 9 minutes to fill up the whole tank when all pipes are opened.