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Two pipes A and B can fill a tank in 20 and 30 minutes respectively. Both the pipes are opened together but after 5 minutes pipe B is closed. What is the total time required to fill the tank
- a)16.1/3 min
- b)16.2/3 min
- c)17.2/3 min
- d)18.2/3 min
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. B...
(1/20 + 1/30)*5 + (1/20)*T = 1
total time = T + 5 min
total time = T + 5 min
Most Upvoted Answer
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. B...
Given:
Pipe A can fill the tank in 20 minutes.
Pipe B can fill the tank in 30 minutes.
Both pipes A and B are opened together but after 5 minutes, pipe B is closed.
To find:
The total time required to fill the tank.
Approach:
We can find the rate at which each pipe fills the tank and then calculate the combined rate when both pipes are opened together.
Let's assume the capacity of the tank is 1 unit.
Rate of pipe A = 1/20 units per minute (as it can fill the tank in 20 minutes)
Rate of pipe B = 1/30 units per minute (as it can fill the tank in 30 minutes)
Combined rate when both pipes are opened together = Rate of pipe A + Rate of pipe B
After 5 minutes, pipe B is closed. So, only pipe A is filling the tank.
Let's calculate the amount of water filled by pipe A in 5 minutes:
Amount of water filled by pipe A = Rate of pipe A * Time
= (1/20) * 5
= 1/4 units
Remaining capacity of the tank = Total capacity - Amount of water filled by pipe A
= 1 - 1/4
= 3/4 units
Now, only pipe A is filling the remaining 3/4 units of the tank.
Time taken by pipe A to fill 3/4 units of the tank = (3/4) / Rate of pipe A
= (3/4) / (1/20)
= (3/4) * (20/1)
= 15 minutes
Total time required to fill the tank = Time taken by pipe A to fill 5 minutes + Time taken by pipe A to fill 3/4 units of the tank
= 5 minutes + 15 minutes
= 20 minutes
Therefore, the total time required to fill the tank is 20 minutes, which is equivalent to 16 2/3 minutes. Hence, option B is the correct answer.
Pipe A can fill the tank in 20 minutes.
Pipe B can fill the tank in 30 minutes.
Both pipes A and B are opened together but after 5 minutes, pipe B is closed.
To find:
The total time required to fill the tank.
Approach:
We can find the rate at which each pipe fills the tank and then calculate the combined rate when both pipes are opened together.
Let's assume the capacity of the tank is 1 unit.
Rate of pipe A = 1/20 units per minute (as it can fill the tank in 20 minutes)
Rate of pipe B = 1/30 units per minute (as it can fill the tank in 30 minutes)
Combined rate when both pipes are opened together = Rate of pipe A + Rate of pipe B
After 5 minutes, pipe B is closed. So, only pipe A is filling the tank.
Let's calculate the amount of water filled by pipe A in 5 minutes:
Amount of water filled by pipe A = Rate of pipe A * Time
= (1/20) * 5
= 1/4 units
Remaining capacity of the tank = Total capacity - Amount of water filled by pipe A
= 1 - 1/4
= 3/4 units
Now, only pipe A is filling the remaining 3/4 units of the tank.
Time taken by pipe A to fill 3/4 units of the tank = (3/4) / Rate of pipe A
= (3/4) / (1/20)
= (3/4) * (20/1)
= 15 minutes
Total time required to fill the tank = Time taken by pipe A to fill 5 minutes + Time taken by pipe A to fill 3/4 units of the tank
= 5 minutes + 15 minutes
= 20 minutes
Therefore, the total time required to fill the tank is 20 minutes, which is equivalent to 16 2/3 minutes. Hence, option B is the correct answer.
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Community Answer
Two pipes A and B can fill a tank in 20 and 30 minutes respectively. B...
(1/20 + 1/30)*5 + (1/20)*T = 1
total time = T + 5 min
total time = T + 5 min
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