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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: There are two inlet pipes A, B and two outlet pipes C, D inlet pipe B takes 7 hours more to fill the tank when compared to A. Two outlet pipes when working together can empty the tank in 3.5 hours and efficiency of both the pipe is same if all of them working together can fill the tank in 2 hours. Calculate the time taken by A to fill the tank. Quantity B: The ratio of efficiencies of two pipes A and B is in the ratio 3 ∶ 2 and that of pipe B and C is 1 ∶ 3. Pipe A and B are inlet pipes, pipe C is outlet pipe working together they can fill the tank in 7.5 hours. Calculate the time taken by A to fill the tank when working alone.

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: There are two inlet pipes A, B and two outlet pipes C, D inlet pipe B takes 7 hours more to fill the tank when compared to A. Two outlet pipes when working together can empty the tank in 3.5 hours and efficiency of both the pipe is same if all of them working together can fill the tank in 2 hours. Calculate the time taken by A to fill the tank. Quantity B: The ratio of efficiencies of two pipes A and B is in the ratio 3 ∶ 2 and that of pipe B and C is 1 ∶ 3. Pipe A and B are inlet pipes, pipe C is outlet pipe working together they can fill the tank in 7.5 hours. Calculate the time taken by A to fill the tank when working alone. Correct Answer Quantity A < Quantity B

Quantity A:

Time taken by A to fill the tank = x hours

⇒ Tank filled by A in 1 hour = 1/x

Time taken by B to fill the tank = (x + 7) hours

⇒ Tank filled by B in 1 hour = 1/(x + 7)

Two outlet pipes can empty the tank in 3.5 hours and their efficiency is same

⇒ C + D = 1/3.5

⇒ 2C = 1/3.5      ----(C = D)

⇒ C = 1/7

∴ C = D = 7 hours

Working together they can fill the tank in 2 hours

⇒ 1/A + 1/B – 1/C – 1/D = 1/2

⇒ 1/x + 1/(x + 7) – (1/7) – (1/7) = 1/2

⇒ 1/x + 1/x + 7 = 1/2 – 1/7 – 1/7

⇒ (2x + 7)/(x)(x + 7) = 3/14

⇒ 3x2 – 7x – 98 = 0

⇒ 3x2 – 21x + 14x – 98 = 0

⇒ 3x(x – 7) + 14(x – 7) = 0

⇒ x = 7, -14/3

 Rejecting -14/3 as work can’t be negative

∴ Time taken by A to fill the tank alone = 7 hrs

Quantity B:

 The ratio of efficiencies of two pipes A and B is in the ratio 3 ∶ 2

The ratio of efficiencies of two pipes B and C is in the ratio 1 ∶ 3

Equating the coefficient of B in both the ratios

The ratio of efficiencies of two pipes B and C = 2 ∶ 6

∴ Ratio of efficiency of A, B and C = 3 ∶ 2 ∶ 6

Let the time taken by A, B and C be 3x, 2x and 6x

Working together they can fill the tank in 7.5 hours

⇒ 1/3x + 1/2x – 1/6x = 1/7.5

⇒ 4/6x = 1/7.5

⇒ x = 5

∴ Time taken by A to fill the tank alone = 5 × 3 = 15 hours

Hence Quantity A < Quantity B

Related Questions

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