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Pipe A requires 50% less time to fill up the tank then pipe C. Ratio of time required by pipe B to fill up the tank and time required by pipe C to fill up the tank is 4 : 5. If total time taken to fill up the tank is 4 minutes when all the pipes are open. Find the difference between time taken by C and time taken by B to fill up the tank.

Pipe A requires 50% less time to fill up the tank then pipe C. Ratio of time required by pipe B to fill up the tank and time required by pipe C to fill up the tank is 4 : 5. If total time taken to fill up the tank is 4 minutes when all the pipes are open. Find the difference between time taken by C and time taken by B to fill up the tank. Correct Answer 3 minutes

Given:

Pipe C = Pipe A + 50% time less

Pipe B: Pipe C = 4 : 5

Time taken to fill tank = 4 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 C be X

⇒ Time taken by pipe B is 4 × X/ 5

⇒ Time taken by C = Times taken by A + (Time taken by A × 0.50)

⇒ Time taken by C = 1.5 × time taken by A

⇒ Time taken by A = X/ 1.5

Now, placing all variables in formula

⇒ 1/ 4 = (1/ X) + (5/4X) + (1.5/X)

⇒ 1/ 4 = (4 + 5 + 6)/(4X)

⇒ X = 15

⇒ Time taken by pipe B = 4 × 15/5

⇒ Time taken by pipe B = 12 minutes

⇒ Time taken by pipe A = 15/1.5

⇒ Time taken by pipe A = 10 minutes

⇒ required difference = 15 – 12

∴ required difference is 3 minutes

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