Pipe P alone can fill a tank in 5 minutes and pipe Q alone can fill it

Pipe P alone can fill a tank in 5 minutes and pipe Q alone can fill it in 4 minutes. Pipe R alone can empty the same tank in 2 minutes. Pipe P and Q are opened together to fill the tank. After 2 minutes, pipe R is also opened. How much time pipe R will take to empty this tank? 1. 18 Minutes2. 15 Minutes3. 12 Minutes4. 20 Minutes

Answer» Correct Answer - Option 1 : 18 Minutes

Given:

Pipe P can fill a tank in 5 minutes

Pipe Q can fill a tank in 4 minutes

Pipe R can empty a tank in 2 minutes

Calculation:

Pipe	Time	Total Work = LCM (5, 4 and 2)	Efficiency(No. of units worked in a day)
P	5		20 ÷ 5 = 4
Q	4	20	20 ÷ 4 = 5
R	(2)		20 ÷ 2 = (10)
P+ Q + (-R)			4 + 5 -10 = (1) Work done by all three pipes in a minute

⇒ Work done by (P + Q) in first 2 minutes = (4 + 5) × 2 = 18 units

⇒ Work done by (P+ Q – R) = 18/(1)

∴ R will take 18 minutes to empty the tank.

The Correct option is 1 i.e. 18 minutes.

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