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Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 8 hours to fill up the whole tank. After how many hours Q was closed?
  • a)
    4 hours
  • b)
    5 hours
  • c)
    2 hours
  • d)
    6 hours
  • e)
    None of the Above
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two pipes P and Q can fill a cistern in 10 hours and 20 hours respecti...
Pipe P Efficiency = 100/10 = 10%
Pipe Q Efficiency = 100/20 = 5%
Net Efficiency = 15%
15x + 10(8-x) = 100
x = 4
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Most Upvoted Answer
Two pipes P and Q can fill a cistern in 10 hours and 20 hours respecti...
Pipe P Efficiency = 100/10 = 10%
Pipe Q Efficiency = 100/20 = 5%
Net Efficiency = 15%
15x + 10(8-x) = 100
x = 4
Free Test
Community Answer
Two pipes P and Q can fill a cistern in 10 hours and 20 hours respecti...
To solve this problem, we can consider the rates at which the two pipes fill the cistern. Let the rate at which pipe P fills the cistern be x liters per hour, and the rate at which pipe Q fills the cistern be y liters per hour.

Rate of pipe P = 1 cistern / 10 hours = 1/10 cistern per hour = x liters per hour
Rate of pipe Q = 1 cistern / 20 hours = 1/20 cistern per hour = y liters per hour

Since the rates are given in terms of cisterns per hour, we can equate the rates to find the values of x and y:

x = 1/10 cistern per hour
y = 1/20 cistern per hour

Simultaneously filling the cistern:
When both pipes P and Q are opened simultaneously, their rates of filling are additive. Therefore, the combined rate of filling the cistern is:

x + y = 1/10 + 1/20 = 3/20 cistern per hour

After some time, pipe Q is closed. Let's assume that pipe Q was closed after t hours. So, for the first t hours, both pipes P and Q were open, and for the remaining 8 hours, only pipe P was open.

Total time taken to fill the cistern = t + 8 hours
Rate of pipe P = x liters per hour (as pipe Q is closed)
Rate of pipe Q = 0 liters per hour (as pipe Q is closed)

Using the rates, we can set up the following equation based on the principle of work:

(t + 8)(x) = 1 cistern

Simplifying the equation, we get:

(t + 8)(1/10) = 1
(t + 8)/10 = 1
t + 8 = 10
t = 10 - 8
t = 2

Therefore, pipe Q was closed after 2 hours (option C).
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Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 8 hours to fill up the whole tank. After how many hours Q was closed?a)4 hoursb)5 hoursc)2 hoursd)6 hourse)None of the AboveCorrect answer is option 'A'. Can you explain this answer?
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