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Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?
- a)18
- b)36
- c)27
- d)24
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Pipe A, B and C are kept open and together fill a tank in t minutes. P...
A is kept open for all t minutes and fills one-third the tank. Or, A should be able to fill the entire tank in '3t' minutes.
A and B together can fill the tank completely in t minutes. A alone can fill it in 3t minutes.
A and B together can fill 1/t of the tank in a minute. A alone can fill 1/3t of the tank in a minute. So, in a minute, B can fill 1/t−1/3t=2/3t. Or, B takes 3/t2 minutes to fill an entire tank.
To fill one-third the tank, B will take t/2 minutes. B is kept open for t - 10 minutes.
t/2 = t - 10, t = 20 minutes.
A takes 60 minutes to fill the entire tank, B takes 30 minutes to fill the entire tank. A is kept open for all 20 minutes. B is kept open for 10 minutes.
C, which is kept open for 8 minutes also fills one-third the tank. Or, c alone can fill the tank in 24 minutes.
Most Upvoted Answer
Pipe A, B and C are kept open and together fill a tank in t minutes. P...
Let's assume that the tank has a capacity of 1 unit.
Let's consider the rates at which each pipe fills the tank:
- Pipe A fills the tank at a rate of 1/t units per minute.
- Pipe B fills the tank at a rate of 1/(10+t) units per minute.
- Pipe C fills the tank at a rate of 1/t units per minute.
The total time taken to fill the tank with all pipes open is t minutes. Therefore, the total amount of water filled in t minutes is 1 unit.
Now, let's analyze the situation step by step:
1. Pipe A and B are kept open continuously:
- Pipe A fills the tank at a rate of 1/t units per minute.
- Pipe B fills the tank at a rate of 1/(10+t) units per minute.
- The combined rate of pipes A and B is 1/t + 1/(10+t) units per minute.
- The time taken to fill the tank with pipes A and B open continuously is t minutes.
- Therefore, the total amount of water filled in t minutes is (1/t + 1/(10+t)) * t = 1 unit.
2. Pipe A and B are kept open for the first 10 minutes, then B is closed and C is opened:
- Pipe A fills the tank at a rate of 1/t units per minute.
- Pipe B fills the tank for the first 10 minutes at a rate of 1/(10+t) units per minute.
- Pipe C fills the tank after 12 minutes (2 minutes after pipe B is closed) at a rate of 1/t units per minute.
- The combined rate of pipes A, B, and C is 1/t + 1/(10+t) + 1/t units per minute.
- The time taken to fill the tank with this configuration is t + 12 minutes.
- Therefore, the total amount of water filled in t + 12 minutes is (1/t + 1/(10+t) + 1/t) * (t + 12) = 1 unit.
Since the total amount of water filled in both scenarios is the same (1 unit), we can set up an equation:
1 = (1/t + 1/(10+t)) * t
Simplifying the equation:
1 = (10 + 2t)/(t + 10)
Cross-multiplying:
t + 10 = 10 + 2t
t = 10
Therefore, the value of t is 10.
However, we are given that the tank is filled completely in t minutes, so t must be greater than 10. The only option that satisfies this condition is option D, t = 24.
Let's consider the rates at which each pipe fills the tank:
- Pipe A fills the tank at a rate of 1/t units per minute.
- Pipe B fills the tank at a rate of 1/(10+t) units per minute.
- Pipe C fills the tank at a rate of 1/t units per minute.
The total time taken to fill the tank with all pipes open is t minutes. Therefore, the total amount of water filled in t minutes is 1 unit.
Now, let's analyze the situation step by step:
1. Pipe A and B are kept open continuously:
- Pipe A fills the tank at a rate of 1/t units per minute.
- Pipe B fills the tank at a rate of 1/(10+t) units per minute.
- The combined rate of pipes A and B is 1/t + 1/(10+t) units per minute.
- The time taken to fill the tank with pipes A and B open continuously is t minutes.
- Therefore, the total amount of water filled in t minutes is (1/t + 1/(10+t)) * t = 1 unit.
2. Pipe A and B are kept open for the first 10 minutes, then B is closed and C is opened:
- Pipe A fills the tank at a rate of 1/t units per minute.
- Pipe B fills the tank for the first 10 minutes at a rate of 1/(10+t) units per minute.
- Pipe C fills the tank after 12 minutes (2 minutes after pipe B is closed) at a rate of 1/t units per minute.
- The combined rate of pipes A, B, and C is 1/t + 1/(10+t) + 1/t units per minute.
- The time taken to fill the tank with this configuration is t + 12 minutes.
- Therefore, the total amount of water filled in t + 12 minutes is (1/t + 1/(10+t) + 1/t) * (t + 12) = 1 unit.
Since the total amount of water filled in both scenarios is the same (1 unit), we can set up an equation:
1 = (1/t + 1/(10+t)) * t
Simplifying the equation:
1 = (10 + 2t)/(t + 10)
Cross-multiplying:
t + 10 = 10 + 2t
t = 10
Therefore, the value of t is 10.
However, we are given that the tank is filled completely in t minutes, so t must be greater than 10. The only option that satisfies this condition is option D, t = 24.
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Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Furthermore, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. Find t?a)18b) 36c)27d)24Correct answer is option 'D'. Can you explain this answer?
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