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Three pipes x, y and z can fill a tank A can fill it in 4 minutes. Two pipes p and q are connected to tank B. how much time does it take for both tanks to run at the full capacity? Ratio of time taken to fill tank A by P and time taken by x to fill tank A is 2: 1 and ratio of time taken by Q to fill tank B and Z to fill tank A is 5: 3. Pipe P is 20% more efficient then pipe Q. and pipe Y takes 12 minutes to fill the tank. Capacity of tank B is 3/4 times of tank A. Note: Tank B is to be filled only after filling tank A. Valves of pipe p and q are closed once tank B is running at full capacity.

Three pipes x, y and z can fill a tank A can fill it in 4 minutes. Two pipes p and q are connected to tank B. how much time does it take for both tanks to run at the full capacity? Ratio of time taken to fill tank A by P and time taken by x to fill tank A is 2: 1 and ratio of time taken by Q to fill tank B and Z to fill tank A is 5: 3. Pipe P is 20% more efficient then pipe Q. and pipe Y takes 12 minutes to fill the tank. Capacity of tank B is 3/4 times of tank A. Note: Tank B is to be filled only after filling tank A. Valves of pipe p and q are closed once tank B is running at full capacity. Correct Answer 163/ 9 minutes

 

Calculation:

Let, pipe Q take X minutes

⇒ Pipe P = X × 0.80 (∵ It is 20%more efficient hence takes only 80% of time to fill the tank)

⇒ p: x = 2: 1

⇒ p/ x = 2/ 1

⇒ x = 0.8X/ 2

⇒ x = 2X/ 5

⇒ q: z = 5: 3

⇒ X/ Z = 5/ 3

⇒ X × 3/ 5 = Z

⇒ 3X/ 5 = Z

⇒ 1/ 4 = (5/ 2X) + (1/ 12) + (5/ 3X)

⇒ (1/ 4) – (1/ 12) = (5/ 2X) + (5/ 3X)

⇒ 1/ 6 = (25X)/ 6X2

⇒ 6X2 = 25X × 6

⇒ X = 25

Finding values of p, q, x and z

⇒ p = 20 minutes, q = 25 minutes, x = 10 minutes, z = 15 minutes

⇒ Time taken to fill tank A = 4 minutes

⇒ Time taken to fill tank B = T

⇒ 1/ T = (1/ 20) + (1/ 25)

⇒ T = 500/ 45

⇒ T = 100/ 9 minutes

Tank B = 3 × Tank A/ 4

⇒ Water level in tank A after filing tank B = 1/ 4 of its original capacity

⇒ Time taken to fill up rest of tank A = (1 – 1/4) × 4

⇒ Time taken to fill up rest of tank A = 3 minutes

Total time taken = 4 + (100/ 9) + 3

⇒ Total time taken = 163/ 9 minutes

∴ Total time taken to fill tank is 163/ 9 minutes

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