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Ratio of time taken to fill up the tank by pipe B and pipe A is 2 : 1, pipe C requires 2 minutes less then pipe A to empty the whole tank and if all the three pipes are opened together then it requires 40 minutes to fill up the whole tank. Now, if all the pipes are closed after 10 minutes then how much time does pipe B take to fill the whole tank?

Ratio of time taken to fill up the tank by pipe B and pipe A is 2 : 1, pipe C requires 2 minutes less then pipe A to empty the whole tank and if all the three pipes are opened together then it requires 40 minutes to fill up the whole tank. Now, if all the pipes are closed after 10 minutes then how much time does pipe B take to fill the whole tank? Correct Answer 15 minutes

Given:

Pipe B: Pipe A = 2 : 1

Pipe C = Pipe A – 2 minutes

Total time = 40 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)

Calculation:

Let time taken by pipe A be X minutes

⇒ Time taken by pipe B = 2X

⇒ Time taken by pipe C = X – 2

Now, placing them in equation

⇒ 1/ 40 = (1/ X) + (1/ 2X) – (1/ (X – 2))

⇒ 1/ 40 = 2(X – 2) + (X – 2) – 2X/ (2X × (X – 2))

⇒ 2X × (X – 2) = 40X – 240

⇒ X = 10 or 12 (any value of x can be taken)

⇒ Time taken by pipe B to fill the tank alone = 20 minutes

⇒ Time taken by pipe C to empty the tank = 8 minutes

Now, finding number of units filled in one minute

Pipe A = 40/ 10 = 4 units/minute

Pipe B = 40/ 20 = 2 units/minute

Pipe C = 40/ 8 = 5 units/minute

Now, when all three are open together

⇒ Total units filled per minute = 1 unit/ minute

⇒ In 10 minutes = 10 units will be filled

⇒ Remaining units = 30 units/ minutes

⇒ Time taken by pipe B to fill the remaining tank = 30/2

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

∴ Required time is 15 minutes

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