A7 minutes
B12 minutes
C9 minutes
D5 minutes
Answer:
C. 9 minutes
Read Explanation:
Work Rate: The amount of work (filling the tank) done per unit of time.
Combined Rate: When multiple entities work together, their rates add up.
Net Work Done: The sum of work done by each entity.
Individual Pipe Capacities (Work Done in 1 minute):
Pipe A fills 1/7 of the tank per minute.
Pipe B fills 1/21 of the tank per minute.
Combined Rate of Pipes A and B:
Rate (A + B) = Rate (A) + Rate (B) = (1/7) + (1/21)
To add these fractions, find a common denominator, which is 21.
Rate (A + B) = (3/21) + (1/21) = 4/21 of the tank per minute.
Scenario Breakdown:
Both pipes A and B are opened together for some time, let's call this time 'x' minutes.
After 'x' minutes, pipe A is closed.
Pipe B continues to fill the remaining part of the tank alone for some time.
The total time taken to fill the tank is 12 minutes. This means Pipe B was open for the entire 12 minutes.
The time for which Pipe A was open is 'x' minutes.
The time for which Pipe B was open alone is (12 - x) minutes.
Work Done During Combined Operation:
In 'x' minutes, the work done by both pipes together is: Work (A + B) = Rate (A + B) * Time = (4/21) * x = 4x/21
Work Done During Solo Operation of Pipe B:
Pipe B is open alone for (12 - x) minutes.
Work done by Pipe B alone = Rate (B) * Time = (1/21) * (12 - x) = (12 - x)/21
Total Work Done: The sum of work done during the combined operation and the solo operation of Pipe B must equal 1 (representing a completely filled tank).
(4x/21) + ((12 - x)/21) = 1
Multiply the entire equation by 21 to eliminate the denominators: 4x + (12 - x) = 21
Simplify the equation: 3x + 12 = 21
Solve for x: 3x = 21 - 12 => 3x = 9 => x = 3 minutes
Time Pipe B Was Alone:
The question asks for how long Pipe B was *alone* open.
This is calculated as: Total time - Time A was open = 12 minutes - x minutes.
Time B alone = 12 - 3 = 9 minutes.