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Four pipes P, Q, R and S are connected to a tank. Pipe P, Q, R and S can fill the whole tank in 300/37 minutes. Ratio of time taken by pipe P to fill the tank when operating alone and pipe Q to fill the tank when operating alone is 3 : 2, pipe Q is 20% more efficient then pipe R and time taken by pipe S is 10 minutes more than pipe R. Find difference between time taken by pipe Q and pipe P to fill up the tank alone. 

Four pipes P, Q, R and S are connected to a tank. Pipe P, Q, R and S can fill the whole tank in 300/37 minutes. Ratio of time taken by pipe P to fill the tank when operating alone and pipe Q to fill the tank when operating alone is 3 : 2, pipe Q is 20% more efficient then pipe R and time taken by pipe S is 10 minutes more than pipe R. Find difference between time taken by pipe Q and pipe P to fill up the tank alone.  Correct Answer 10 minutes

Given:

Pipe P: Pipe Q = 3 : 2

Pipe Q = 20% more efficient then pipe R

Pipe S = Pipe R + 10 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)

Calculation:

Let time taken by pipe R = X minutes

⇒ Time taken by pipe Q = X × (1 – 0.20)

⇒ Time taken by pipe Q = 0.80 × X

⇒ Time taken by pipe P = 0.80X × 3/ 2

⇒ Time taken by pipe P = 1.2X

Pipe S = X + 10

⇒ 37/ 300 = (1/X) + (1/ 0.80 X) + (1/ 1.2X) + (1/(X + 10))

⇒ 37/ 300 = (1.2 × (X + 10)) + (1.5 × (X + 10)) + (1 × (X + 10)) + 1.2X/(1.2X × (X + 10))

Solving the above equation,

⇒ X = 25 minutes

⇒ Pipe P = 20 minutes

⇒ Pipe Q = 30 minutes (∵ 1.2 × 25 = 30)

⇒ required difference = 30 – 20

∴ required difference is 10 minutes

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