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If a pipe A can fill a tank 3 times faster than pipe B and takes 32 minutes less than pipe B to fill the tank. If both the pipes are opened simultaneously, then find the time taken to fill the tank?
- a)14 minutes
- b)12 minutes
- c)15 minutes
- d)16 minutes
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If a pipe A can fill a tank 3 times faster than pipe B and takes 32 mi...
3x – x = 32
x = 16
1/16 + 1/48 = 4/48
Time taken to fill the tank = 48/4 = 12 minutes
x = 16
1/16 + 1/48 = 4/48
Time taken to fill the tank = 48/4 = 12 minutes
Most Upvoted Answer
If a pipe A can fill a tank 3 times faster than pipe B and takes 32 mi...
Given information:
- Pipe A fills the tank 3 times faster than pipe B.
- Pipe A takes 32 minutes less than pipe B to fill the tank.
Let's assume that pipe B takes x minutes to fill the tank.
- Pipe A fills the tank 3 times faster than pipe B, so it takes x/3 minutes to fill the tank.
- Pipe A takes 32 minutes less than pipe B to fill the tank, so we can write the equation: x/3 = x - 32.
Now, let's solve the equation to find the value of x.
x/3 = x - 32
Multiplying both sides of the equation by 3 to eliminate the fraction:
x = 3x - 96
Bringing like terms to one side:
2x = 96
Dividing both sides of the equation by 2:
x = 48
So, pipe B takes 48 minutes to fill the tank.
To find the time taken to fill the tank when both pipes A and B are opened simultaneously, we can add their rates.
The rate of pipe A is 1/(x/3) = 3/x tanks per minute.
The rate of pipe B is 1/x tanks per minute.
When both pipes are opened simultaneously, their combined rate is 3/x + 1/x = 4/x tanks per minute.
Therefore, the time taken to fill the tank when both pipes A and B are opened simultaneously is x/4 minutes.
Substituting the value of x, we get:
48/4 = 12 minutes.
Hence, the correct answer is option B) 12 minutes.
- Pipe A fills the tank 3 times faster than pipe B.
- Pipe A takes 32 minutes less than pipe B to fill the tank.
Let's assume that pipe B takes x minutes to fill the tank.
- Pipe A fills the tank 3 times faster than pipe B, so it takes x/3 minutes to fill the tank.
- Pipe A takes 32 minutes less than pipe B to fill the tank, so we can write the equation: x/3 = x - 32.
Now, let's solve the equation to find the value of x.
x/3 = x - 32
Multiplying both sides of the equation by 3 to eliminate the fraction:
x = 3x - 96
Bringing like terms to one side:
2x = 96
Dividing both sides of the equation by 2:
x = 48
So, pipe B takes 48 minutes to fill the tank.
To find the time taken to fill the tank when both pipes A and B are opened simultaneously, we can add their rates.
The rate of pipe A is 1/(x/3) = 3/x tanks per minute.
The rate of pipe B is 1/x tanks per minute.
When both pipes are opened simultaneously, their combined rate is 3/x + 1/x = 4/x tanks per minute.
Therefore, the time taken to fill the tank when both pipes A and B are opened simultaneously is x/4 minutes.
Substituting the value of x, we get:
48/4 = 12 minutes.
Hence, the correct answer is option B) 12 minutes.
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If a pipe A can fill a tank 3 times faster than pipe B and takes 32 minutes less than pipe B to fill the tank. If both the pipes are opened simultaneously, then find the time taken to fill the tank?a)14 minutesb)12 minutesc)15 minutesd)16 minutese)None of the AboveCorrect answer is option 'B'. Can you explain this answer?
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