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Three pipes P, Q and R can fill the tank in 5, 10 and 15 minutes respectively. If all the pipes are opened together and pipe Q is turned off 5 minutes before the tank is fill. Then find the time in which the tank will full.
- a)45/11hrs
- b)53/11hrs
- c)51/13hrs
- d)47/11hrs
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Three pipes P, Q and R can fill the tank in 5, 10 and 15 minutes respe...
Let total time taken by the pipes is T hrs, then
(1/5 + 1/10 + 1/15)*(T – 5) + (1/5 + 1/15)*5 = 1
(1/5 + 1/10 + 1/15)*(T – 5) + (1/5 + 1/15)*5 = 1
Most Upvoted Answer
Three pipes P, Q and R can fill the tank in 5, 10 and 15 minutes respe...
Given Information:
- Pipe P can fill the tank in 5 minutes.
- Pipe Q can fill the tank in 10 minutes.
- Pipe R can fill the tank in 15 minutes.
- Pipe Q is turned off 5 minutes before the tank is filled.
To Find:
The time it takes to fill the tank when all pipes are opened together.
Solution:
To find the time it takes to fill the tank when all pipes are opened together, we need to calculate the combined rate at which the pipes fill the tank.
Let's assume the capacity of the tank is 1 unit.
Rate of Pipe P:
Pipe P can fill the tank in 5 minutes, so its rate of filling is 1/5 units per minute.
Rate of Pipe Q:
Pipe Q can fill the tank in 10 minutes, so its rate of filling is 1/10 units per minute.
Rate of Pipe R:
Pipe R can fill the tank in 15 minutes, so its rate of filling is 1/15 units per minute.
Combined Rate:
When all pipes are opened together, their rates of filling are added.
Combined rate = Rate of Pipe P + Rate of Pipe Q + Rate of Pipe R
= 1/5 + 1/10 + 1/15
= 3/30 + 2/30 + 2/30
= 7/30 units per minute
Time taken to fill the tank:
Let's assume the time taken to fill the tank when all pipes are opened together is T minutes.
In T minutes, the combined rate of filling will fill a fraction of the tank equal to the combined rate multiplied by T.
Fraction of the tank filled in T minutes = Combined rate * T
= (7/30) * T
Since Pipe Q is turned off 5 minutes before the tank is filled, the fraction of the tank filled by Pipe Q alone in T minutes is (1/10) * (T - 5).
The sum of the fractions filled by Pipe Q alone and the combined rate should be equal to 1 (since the tank is full).
(7/30) * T + (1/10) * (T - 5) = 1
Simplifying the equation, we get:
(7/30) * T + (1/10) * T - (1/10) * 5 = 1
(7/30) * T + (1/10) * T - 1/2 = 1
(7/30) * T + (3/30) * T - 1/2 = 1
(10/30) * T - 1/2 = 1
(1/3) * T - 1/2 = 1
(1/3) * T = 1 + 1/2
(1/3) * T = 3/2
T = (3/2) * 3
T = 9/2
T = 4.5 minutes
Result:
The tank will be filled in 4.5 minutes.
Answer:
The correct answer is option A) 45/11 hrs.
- Pipe P can fill the tank in 5 minutes.
- Pipe Q can fill the tank in 10 minutes.
- Pipe R can fill the tank in 15 minutes.
- Pipe Q is turned off 5 minutes before the tank is filled.
To Find:
The time it takes to fill the tank when all pipes are opened together.
Solution:
To find the time it takes to fill the tank when all pipes are opened together, we need to calculate the combined rate at which the pipes fill the tank.
Let's assume the capacity of the tank is 1 unit.
Rate of Pipe P:
Pipe P can fill the tank in 5 minutes, so its rate of filling is 1/5 units per minute.
Rate of Pipe Q:
Pipe Q can fill the tank in 10 minutes, so its rate of filling is 1/10 units per minute.
Rate of Pipe R:
Pipe R can fill the tank in 15 minutes, so its rate of filling is 1/15 units per minute.
Combined Rate:
When all pipes are opened together, their rates of filling are added.
Combined rate = Rate of Pipe P + Rate of Pipe Q + Rate of Pipe R
= 1/5 + 1/10 + 1/15
= 3/30 + 2/30 + 2/30
= 7/30 units per minute
Time taken to fill the tank:
Let's assume the time taken to fill the tank when all pipes are opened together is T minutes.
In T minutes, the combined rate of filling will fill a fraction of the tank equal to the combined rate multiplied by T.
Fraction of the tank filled in T minutes = Combined rate * T
= (7/30) * T
Since Pipe Q is turned off 5 minutes before the tank is filled, the fraction of the tank filled by Pipe Q alone in T minutes is (1/10) * (T - 5).
The sum of the fractions filled by Pipe Q alone and the combined rate should be equal to 1 (since the tank is full).
(7/30) * T + (1/10) * (T - 5) = 1
Simplifying the equation, we get:
(7/30) * T + (1/10) * T - (1/10) * 5 = 1
(7/30) * T + (1/10) * T - 1/2 = 1
(7/30) * T + (3/30) * T - 1/2 = 1
(10/30) * T - 1/2 = 1
(1/3) * T - 1/2 = 1
(1/3) * T = 1 + 1/2
(1/3) * T = 3/2
T = (3/2) * 3
T = 9/2
T = 4.5 minutes
Result:
The tank will be filled in 4.5 minutes.
Answer:
The correct answer is option A) 45/11 hrs.
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Community Answer
Three pipes P, Q and R can fill the tank in 5, 10 and 15 minutes respe...
Let total time taken by the pipes is T hrs, then
(1/5 + 1/10 + 1/15)*(T – 5) + (1/5 + 1/15)*5 = 1
(1/5 + 1/10 + 1/15)*(T – 5) + (1/5 + 1/15)*5 = 1
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