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A large cistern can be filled by two pipes P and Q in 15 minutes and 20 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?
- a)12 minutes
- b)17 minutes
- c)18 minutes
- d)19 minutes
- e)None of the Above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A large cistern can be filled by two pipes P and Q in 15 minutes and 2...
Part filled by P and Q = 1/15 + 1/20 = 7/60
Part filled by Q = 1/20
x/2(7/60 + 1/20) = 12 minutes
Part filled by Q = 1/20
x/2(7/60 + 1/20) = 12 minutes
Most Upvoted Answer
A large cistern can be filled by two pipes P and Q in 15 minutes and 2...
Part filled by P and Q = 1/15 + 1/20 = 7/60
Part filled by Q = 1/20
x/2(7/60 + 1/20) = 12 minutes
Part filled by Q = 1/20
x/2(7/60 + 1/20) = 12 minutes
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Community Answer
A large cistern can be filled by two pipes P and Q in 15 minutes and 2...
To solve this problem, we can use the concept of work. The work done by a pipe is inversely proportional to the time it takes to fill the cistern.
Let's assume that the capacity of the cistern is 1 unit.
Work done by pipe P in 1 minute = 1/15
Work done by pipe Q in 1 minute = 1/20
Work done by pipe Q in half the time = (1/20) * (1/2) = 1/40
Now, let's assume that it takes 'x' minutes to fill the cistern when Q is used for half the time and P and Q fill it together for the other half.
Work done by pipe P in x minutes = (1/15) * (x/2) = x/30
Work done by pipe Q in x minutes = (1/20) * (x/2) = x/40
The total work done by both pipes together is the sum of their individual work:
x/30 + x/40 = 1
To solve this equation, we need to find the least common multiple (LCM) of 30 and 40, which is 120. Multiplying both sides of the equation by 120, we get:
4x + 3x = 120
7x = 120
x = 120/7
Therefore, it will take approximately 17.14 minutes to fill the cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half.
Since we are looking for the closest whole number, the answer is 17 minutes, which corresponds to option A.
Let's assume that the capacity of the cistern is 1 unit.
Work done by pipe P in 1 minute = 1/15
Work done by pipe Q in 1 minute = 1/20
Work done by pipe Q in half the time = (1/20) * (1/2) = 1/40
Now, let's assume that it takes 'x' minutes to fill the cistern when Q is used for half the time and P and Q fill it together for the other half.
Work done by pipe P in x minutes = (1/15) * (x/2) = x/30
Work done by pipe Q in x minutes = (1/20) * (x/2) = x/40
The total work done by both pipes together is the sum of their individual work:
x/30 + x/40 = 1
To solve this equation, we need to find the least common multiple (LCM) of 30 and 40, which is 120. Multiplying both sides of the equation by 120, we get:
4x + 3x = 120
7x = 120
x = 120/7
Therefore, it will take approximately 17.14 minutes to fill the cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half.
Since we are looking for the closest whole number, the answer is 17 minutes, which corresponds to option A.
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