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A cistern is filled by 3 pipes A, B and C with uniform flow. The second pipe B takes3/2 times the time taken by A to fill the tank, while C takes twice the time taken by B to fill the tank. If all the three pipes can fill the tank in 7 hours, find the time required by pipe A alone to fill the tank.
- a)10hrs
- b)12hrs
- c)14hrs
- d)15hrs
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A cistern is filled by 3 pipes A, B and C with uniform flow. The secon...
1/x + 1/ (3/2x) + ½(3x/2) = 1/7
6/3x = 1/7
3x/6 = 7
3x=42
X=14
6/3x = 1/7
3x/6 = 7
3x=42
X=14
Most Upvoted Answer
A cistern is filled by 3 pipes A, B and C with uniform flow. The secon...
1/x + 1/ (3/2x) + ½(3x/2) = 1/7
6/3x = 1/7
3x/6 = 7
3x=42
X=14
6/3x = 1/7
3x/6 = 7
3x=42
X=14
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Community Answer
A cistern is filled by 3 pipes A, B and C with uniform flow. The secon...
To solve this problem, let's assume that the time taken by pipe A to fill the tank is 'x' hours.
Given that pipe B takes 3/2 times the time taken by A to fill the tank, we can conclude that pipe B takes (3/2)x hours to fill the tank.
Similarly, pipe C takes twice the time taken by B to fill the tank, which means pipe C takes 2 * (3/2)x = 3x hours to fill the tank.
Now, let's consider the rate at which each pipe fills the tank. Since all three pipes are filling the tank simultaneously, the combined rate of all three pipes is 1 tank per 7 hours.
The rate of pipe A is 1/x, the rate of pipe B is 1/(3/2)x = 2/3x, and the rate of pipe C is 1/(3x).
Adding up the rates of all three pipes, we get:
1/x + 2/3x + 1/(3x) = 1/7
To simplify the equation, we can multiply each term by the least common multiple of the denominators, which is 3x:
3 + 2 + 1 = 3x/7
6 = 3x/7
Cross-multiplying the equation, we get:
3x = 42
x = 14
Therefore, pipe A alone takes 14 hours to fill the tank.
Hence, the correct answer is option C) 14 hours.
Given that pipe B takes 3/2 times the time taken by A to fill the tank, we can conclude that pipe B takes (3/2)x hours to fill the tank.
Similarly, pipe C takes twice the time taken by B to fill the tank, which means pipe C takes 2 * (3/2)x = 3x hours to fill the tank.
Now, let's consider the rate at which each pipe fills the tank. Since all three pipes are filling the tank simultaneously, the combined rate of all three pipes is 1 tank per 7 hours.
The rate of pipe A is 1/x, the rate of pipe B is 1/(3/2)x = 2/3x, and the rate of pipe C is 1/(3x).
Adding up the rates of all three pipes, we get:
1/x + 2/3x + 1/(3x) = 1/7
To simplify the equation, we can multiply each term by the least common multiple of the denominators, which is 3x:
3 + 2 + 1 = 3x/7
6 = 3x/7
Cross-multiplying the equation, we get:
3x = 42
x = 14
Therefore, pipe A alone takes 14 hours to fill the tank.
Hence, the correct answer is option C) 14 hours.
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A cistern is filled by 3 pipes A, B and C with uniform flow. The second pipe B takes3/2 times the time taken by A to fill the tank, while C takes twice the time taken by B to fill the tank. If all the three pipes can fill the tank in 7 hours, find the time required by pipe A alone to fill the tank.a)10hrsb)12hrsc)14hrsd)15hrse)None of theseCorrect answer is option 'C'. Can you explain this answer?
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Solutions for A cistern is filled by 3 pipes A, B and C with uniform flow. The second pipe B takes3/2 times the time taken by A to fill the tank, while C takes twice the time taken by B to fill the tank. If all the three pipes can fill the tank in 7 hours, find the time required by pipe A alone to fill the tank.a)10hrsb)12hrsc)14hrsd)15hrse)None of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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ample number of questions to practice A cistern is filled by 3 pipes A, B and C with uniform flow. The second pipe B takes3/2 times the time taken by A to fill the tank, while C takes twice the time taken by B to fill the tank. If all the three pipes can fill the tank in 7 hours, find the time required by pipe A alone to fill the tank.a)10hrsb)12hrsc)14hrsd)15hrse)None of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Quant tests.
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