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Two pipes P and Q can fill a tank in 20m and 30m respectively. If both the pipes are opened simultaneously, after how much time should Q be closed so that the tank is full in 16minutes ?
- a)12min
- b)6min
- c)10min
- d)7min
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two pipes P and Q can fill a tank in 20m and 30m respectively. If both...
X(1/20+1/30) +(16-x)1/20 = 1
5x/60+16-x/20 =1
5x+48-3x/60 =1
2x+48 = 60
2x=12
X=12/2 = 6
5x/60+16-x/20 =1
5x+48-3x/60 =1
2x+48 = 60
2x=12
X=12/2 = 6
Most Upvoted Answer
Two pipes P and Q can fill a tank in 20m and 30m respectively. If both...
In 1min
part of tank filled by p= 1/20
,,. ,,,. ,,,,. q = 1/30
,,,,. ,,,,. by p and q both = 1/12
let after x minutes q is closed
x/12 + (16-x)/20 = 1
x = 6 minutes
part of tank filled by p= 1/20
,,. ,,,. ,,,,. q = 1/30
,,,,. ,,,,. by p and q both = 1/12
let after x minutes q is closed
x/12 + (16-x)/20 = 1
x = 6 minutes
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Community Answer
Two pipes P and Q can fill a tank in 20m and 30m respectively. If both...
To solve this problem, we need to determine the rate at which each pipe can fill the tank and then calculate the time it would take for each pipe to fill the tank individually.
Let's assume that the tank has a capacity of 1 unit.
Rate of filling for pipe P = 1/20 units per minute
Rate of filling for pipe Q = 1/30 units per minute
Now, let's calculate the time it would take for each pipe to fill the tank individually:
Time taken by pipe P to fill the tank = 1 unit / (1/20 units per minute) = 20 minutes
Time taken by pipe Q to fill the tank = 1 unit / (1/30 units per minute) = 30 minutes
As per the question, we need to find out after how much time pipe Q should be closed so that the tank is full in 16 minutes.
Let's assume that pipe Q is closed after 'x' minutes.
So, the time for which both pipes are open = 16 minutes - x minutes.
During this time, pipe P will fill the tank at a rate of 1/20 units per minute, and pipe Q will fill the tank at a rate of 1/30 units per minute.
The combined rate of filling the tank when both pipes are open = 1/20 + 1/30 units per minute = 1/12 units per minute
Now, we need to calculate the amount of water filled in the tank during the time both pipes are open.
Amount of water filled = rate of filling x time
= (1/12 units per minute) x (16 - x) minutes
= (16 - x) / 12 units
Since the tank is full when the amount of water filled is equal to 1 unit, we can set up the following equation:
(16 - x) / 12 = 1
16 - x = 12
x = 16 - 12
x = 4
Therefore, pipe Q should be closed after 4 minutes so that the tank is full in 16 minutes.
Hence, the correct answer is option B) 6 minutes.
Let's assume that the tank has a capacity of 1 unit.
Rate of filling for pipe P = 1/20 units per minute
Rate of filling for pipe Q = 1/30 units per minute
Now, let's calculate the time it would take for each pipe to fill the tank individually:
Time taken by pipe P to fill the tank = 1 unit / (1/20 units per minute) = 20 minutes
Time taken by pipe Q to fill the tank = 1 unit / (1/30 units per minute) = 30 minutes
As per the question, we need to find out after how much time pipe Q should be closed so that the tank is full in 16 minutes.
Let's assume that pipe Q is closed after 'x' minutes.
So, the time for which both pipes are open = 16 minutes - x minutes.
During this time, pipe P will fill the tank at a rate of 1/20 units per minute, and pipe Q will fill the tank at a rate of 1/30 units per minute.
The combined rate of filling the tank when both pipes are open = 1/20 + 1/30 units per minute = 1/12 units per minute
Now, we need to calculate the amount of water filled in the tank during the time both pipes are open.
Amount of water filled = rate of filling x time
= (1/12 units per minute) x (16 - x) minutes
= (16 - x) / 12 units
Since the tank is full when the amount of water filled is equal to 1 unit, we can set up the following equation:
(16 - x) / 12 = 1
16 - x = 12
x = 16 - 12
x = 4
Therefore, pipe Q should be closed after 4 minutes so that the tank is full in 16 minutes.
Hence, the correct answer is option B) 6 minutes.
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