In what time a cistern is filled by three pipes of diameter 2cm, 4cm and 6cm respectively. If the time taken by largest pipe to fill the tank is 40 minutes. Amount of water flowing through the pipe is proportional to the diameter of the pipea)25.5/7 minb)25.3/7 minc)23.5/7 mind)23.4/7 mine)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Given that the diameters of the three pipes are 2 cm, 3 cm and 4 cm

From the given data,

Amount of water from three pipes is 4 units, 9 units and 16 units.

Let the capacity of cistern be 'p' units.

∴ p/58 = 16

⇒ p = 928 units.

In 1 minute, quantity to be filled by 3 pipes = 29 units

∴ Total time required = 928/29 = 32 minutes.

Answer

Let amount of water flowing through pipe is directly proportional to square of radius.

Therefore, for pipe A capacity per min.= 9 units.
for pipe B = 4 units.
for pipe C = 1 units.
Therefore, Total work = 360
when all pipes will work together then work done per min. will be 1+4+9 =14 units.
Therefore time taken= 360/14=25.5/7

Answer

To solve this problem, we need to find the time it takes for the cistern to be filled by three pipes of different diameters. We are given that the largest pipe takes 40 minutes to fill the tank, and the amount of water flowing through the pipe is proportional to the diameter of the pipe.

Let's assume that the diameters of the three pipes are D1, D2, and D3, respectively. According to the given information, the amount of water flowing through each pipe is proportional to its diameter. Therefore, we can say:

Amount of water flowing through pipe 1 (D1) / Time taken by pipe 1 (T1) = Amount of water flowing through pipe 2 (D2) / Time taken by pipe 2 (T2) = Amount of water flowing through pipe 3 (D3) / Time taken by pipe 3 (T3)

We are given that the time taken by the largest pipe (D3) is 40 minutes. Let's assume that the time taken by the other two pipes is T1 and T2.

Using the proportionality equation, we can write:

D1 / T1 = D3 / 40 ...(1)
D2 / T2 = D3 / 40 ...(2)

We are also given that the diameters of the three pipes are in the ratio of 1:2:3. Let's assume the diameter of the smallest pipe (D1) is x cm. Therefore, the diameters of the other two pipes would be 2x cm and 3x cm.

Substituting these values into equations (1) and (2), we get:

x / T1 = 3x / 40 ...(3)
2x / T2 = 3x / 40 ...(4)

Simplifying equations (3) and (4), we get:

1 / T1 = 3 / 40 ...(5)
2 / T2 = 3 / 40 ...(6)

Cross-multiplying equations (5) and (6), we get:

T1 = 40 / 3 ...(7)
T2 = 80 / 3 ...(8)

Now, we need to find the time taken for all three pipes to fill the cistern together. Let's assume this time is T.

Using the proportionality equation, we can write:

D1 / T1 + D2 / T2 + D3 / 40 = 1 / T

Substituting the values of D1, D2, and T1, T2 from above, we get:

x / (40 / 3) + 2x / (80 / 3) + 3x / 40 = 1 / T

Simplifying the equation, we get:

3x/40 + 3x/40 + 3x/40 = 1 / T

9x / 40 = 1 / T

Cross-multiplying the equation, we get:

T = 40 / 9

Converting the time to minutes, we get:

T = 40 / 9 * 60 = 25.5 minutes

Therefore, the time taken for the cistern to be filled by the three pipes is 25.5 minutes. Hence, the correct answer is option A) 25.5/7 minutes

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