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A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?
- a)11 minutes
- b)10 minutes
- c)9 minutes
- d)13 minutes
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A water tank can be filled with two pipes, P and Q, in 20 minutes and...
To solve this problem, we need to calculate the individual rates at which pipes P and Q fill the tank and then determine the time taken by each pipe separately when their efficiency is decreased. Let's break down the solution into steps:
Step 1: Calculate the individual rates at which pipes P and Q fill the tank.
Let the rate at which pipe P fills the tank be x units per minute.
Therefore, the rate at which pipe Q fills the tank is (1/x) units per minute.
Given that pipe P takes 20 minutes and pipe Q takes 25 minutes to fill the tank, we can set up the following equation:
20x + 25(1/x) = 1 (as the tank is filled completely in 1 minute)
Simplifying this equation, we get:
20x^2 + 25 = x
20x^2 - x + 25 = 0
Step 2: Solve the quadratic equation.
Using the quadratic formula, we can find the value of x:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 20, b = -1, and c = 25. Substituting these values into the quadratic formula, we get:
x = (1 ± √(1 - 4(20)(25))) / (2(20))
x = (1 ± √(-1999)) / 40
Since we cannot take the square root of a negative number in real numbers, we can conclude that there is no real value for x. This means that the given information is inconsistent, and the problem cannot be solved.
Therefore, the answer cannot be determined and the correct option is 'None of the above'.
Step 1: Calculate the individual rates at which pipes P and Q fill the tank.
Let the rate at which pipe P fills the tank be x units per minute.
Therefore, the rate at which pipe Q fills the tank is (1/x) units per minute.
Given that pipe P takes 20 minutes and pipe Q takes 25 minutes to fill the tank, we can set up the following equation:
20x + 25(1/x) = 1 (as the tank is filled completely in 1 minute)
Simplifying this equation, we get:
20x^2 + 25 = x
20x^2 - x + 25 = 0
Step 2: Solve the quadratic equation.
Using the quadratic formula, we can find the value of x:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 20, b = -1, and c = 25. Substituting these values into the quadratic formula, we get:
x = (1 ± √(1 - 4(20)(25))) / (2(20))
x = (1 ± √(-1999)) / 40
Since we cannot take the square root of a negative number in real numbers, we can conclude that there is no real value for x. This means that the given information is inconsistent, and the problem cannot be solved.
Therefore, the answer cannot be determined and the correct option is 'None of the above'.
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A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer?
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A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer?.
A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer?.
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A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A water tank can be filled with two pipes, P and Q, in 20 minutes and 25 minutes, respectively. Both pipes are opened together but due to some technical problem, the efficiency of pipes is decreased by 40% and 50%, respectively. After some time, the problem is resolved and the total time taken to fill the tank is 16 minutes now. How long did the problem persist?a)11 minutesb)10 minutesc)9 minutesd)13 minutesCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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