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Two pipes A and B can fill an empty tank in 8 hours and 12 hours respectively. They have opened alternately for 1 hour each, starting with pipe A first. In how many hours will the empty tank be filled?
- a)9(1/4)
- b)9
- c)9(1/3)
- d)9(1/2)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Two pipes A and B can fill an empty tank in 8 hours and 12 hours respe...
Given:
Pipe A alone can fill the tank = 8 hrs
Pipe B alone can fill the tank = 12 hrs
Time ratio of Pipe A and B = 8 ∶ 12 = 2 ∶ 3
Concept used:
Efficiency is inversely proportional to time.
Calculation:
Efficiency ratio of pipe A and B = 3 ∶ 2
Total work = 3 × 8 = 24
Both pipes opened alternately for 1 hr.
Total work in 2 hrs = 3 + 2 = 5
Work in 8 hrs = 5 × 4 = 20
Work in next 1 hr (9th) = 20 + 3 = 23
Remaining work = 24 - 23 = 1
B alone can work in 1 hr = 2
B alone can work in 1/2 hr = 1
So, the total work complete in 9(1/2) hrs.
Pipe A alone can fill the tank = 8 hrs
Pipe B alone can fill the tank = 12 hrs
Time ratio of Pipe A and B = 8 ∶ 12 = 2 ∶ 3
Concept used:
Efficiency is inversely proportional to time.
Calculation:
Efficiency ratio of pipe A and B = 3 ∶ 2
Total work = 3 × 8 = 24
Both pipes opened alternately for 1 hr.
Total work in 2 hrs = 3 + 2 = 5
Work in 8 hrs = 5 × 4 = 20
Work in next 1 hr (9th) = 20 + 3 = 23
Remaining work = 24 - 23 = 1
B alone can work in 1 hr = 2
B alone can work in 1/2 hr = 1
So, the total work complete in 9(1/2) hrs.
Most Upvoted Answer
Two pipes A and B can fill an empty tank in 8 hours and 12 hours respe...
Understanding the Problem
To solve the problem, we need to determine how much of the tank is filled by pipes A and B when they are opened alternately for 1 hour each.
Pipe Filling Rates
- Pipe A fills the tank in 8 hours. Therefore, in 1 hour, it fills 1/8 of the tank.
- Pipe B fills the tank in 12 hours. Therefore, in 1 hour, it fills 1/12 of the tank.
Combining Their Contributions
In a 2-hour cycle (1 hour of A and 1 hour of B):
- Pipe A fills 1/8 of the tank in the first hour.
- Pipe B fills 1/12 of the tank in the second hour.
The total amount filled in 2 hours is:
1/8 + 1/12
To add these fractions, we need a common denominator, which is 24:
- 1/8 = 3/24
- 1/12 = 2/24
So,
Total filled in 2 hours = 3/24 + 2/24 = 5/24 of the tank.
Calculating Total Time
Now, we need to find out how many such cycles are required to fill the tank completely:
- In 2 hours, 5/24 of the tank is filled.
- To fill the entire tank (1), we can set up the equation:
Let x be the number of cycles (2 hours each).
(5/24)x = 1
Solving for x:
x = 24/5 = 4.8 cycles.
Since each cycle is 2 hours, total time for 4.8 cycles:
Total Time = 4.8 * 2 = 9.6 hours.
Final Adjustment
Since 0.6 cycles equal 1.2 hours (0.6 * 2), we need to fill the remaining part of the tank after 9 hours:
- After 9 hours, the tank is filled by 5/24 * 4 = 20/24.
- Remaining = 1 - 20/24 = 4/24 = 1/6 of the tank.
In the next hour (Pipe A), it can fill 1/8, which is more than 1/6.
Thus, the tank will be completely filled in:
Final Answer
9 hours + 1/2 hour = 9(1/2) hours.
The correct answer is option 'D', 9(1/2) hours.
To solve the problem, we need to determine how much of the tank is filled by pipes A and B when they are opened alternately for 1 hour each.
Pipe Filling Rates
- Pipe A fills the tank in 8 hours. Therefore, in 1 hour, it fills 1/8 of the tank.
- Pipe B fills the tank in 12 hours. Therefore, in 1 hour, it fills 1/12 of the tank.
Combining Their Contributions
In a 2-hour cycle (1 hour of A and 1 hour of B):
- Pipe A fills 1/8 of the tank in the first hour.
- Pipe B fills 1/12 of the tank in the second hour.
The total amount filled in 2 hours is:
1/8 + 1/12
To add these fractions, we need a common denominator, which is 24:
- 1/8 = 3/24
- 1/12 = 2/24
So,
Total filled in 2 hours = 3/24 + 2/24 = 5/24 of the tank.
Calculating Total Time
Now, we need to find out how many such cycles are required to fill the tank completely:
- In 2 hours, 5/24 of the tank is filled.
- To fill the entire tank (1), we can set up the equation:
Let x be the number of cycles (2 hours each).
(5/24)x = 1
Solving for x:
x = 24/5 = 4.8 cycles.
Since each cycle is 2 hours, total time for 4.8 cycles:
Total Time = 4.8 * 2 = 9.6 hours.
Final Adjustment
Since 0.6 cycles equal 1.2 hours (0.6 * 2), we need to fill the remaining part of the tank after 9 hours:
- After 9 hours, the tank is filled by 5/24 * 4 = 20/24.
- Remaining = 1 - 20/24 = 4/24 = 1/6 of the tank.
In the next hour (Pipe A), it can fill 1/8, which is more than 1/6.
Thus, the tank will be completely filled in:
Final Answer
9 hours + 1/2 hour = 9(1/2) hours.
The correct answer is option 'D', 9(1/2) hours.
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