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Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank will be filled?
- a)7 hrs
- b)8 hrs
- c)7 hrs. 30 min.
- d)8 hrs. 30 min.
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two pipes can fill a tank in 10 hours and 12 hours respectively, while...
Time taken by A , B and C to fill/empty the tank completely = 10 , 12 and 20 hours respectively
Hence part of tank filled by A, B and emptied by C in 1 hour = 1/10, 1/12 and 1/20 respectively
Part of tank filled by all 3 pipes in 1 min =1/10+1/12−1/20=1/10+1/12−1/20
=660+560−360=660+560−360
=860=860
= 2/15
Hence it will take 15/2 hours ie 7 hours and 30 mins to completely fill the tank
Most Upvoted Answer
Two pipes can fill a tank in 10 hours and 12 hours respectively, while...
Given:
- The first pipe fills the tank in 10 hours.
- The second pipe fills the tank in 12 hours.
- The third pipe empties the tank in 20 hours.
To find:
- The time taken to fill the tank when all three pipes operate simultaneously.
Approach:
- Let's assume the capacity of the tank is 1 unit.
- We need to find the time taken to fill the tank, so let's consider the filling rate of each pipe per hour.
Calculation:
- The first pipe fills 1/10th of the tank in one hour. (Rate: 1/10)
- The second pipe fills 1/12th of the tank in one hour. (Rate: 1/12)
- The third pipe empties 1/20th of the tank in one hour. (Rate: -1/20)
- When all three pipes operate simultaneously, the net filling rate of the tank is the sum of the individual rates.
Net filling rate = (1/10) + (1/12) + (-1/20)
= 1/10 + 1/12 - 1/20
= 12/120 + 10/120 - 6/120
= 16/120
= 4/30
= 2/15
- The net filling rate of the tank is 2/15th of the tank per hour.
- To find the time taken to fill the tank completely, we need to divide the tank's capacity (1 unit) by the net filling rate.
Time taken = (Tank capacity)/(Net filling rate)
= 1 / (2/15)
= 15/2
= 7.5 hours
= 7 hours and 30 minutes
Answer:
Therefore, when all three pipes operate simultaneously, the tank will be filled in 7 hours and 30 minutes.
- The first pipe fills the tank in 10 hours.
- The second pipe fills the tank in 12 hours.
- The third pipe empties the tank in 20 hours.
To find:
- The time taken to fill the tank when all three pipes operate simultaneously.
Approach:
- Let's assume the capacity of the tank is 1 unit.
- We need to find the time taken to fill the tank, so let's consider the filling rate of each pipe per hour.
Calculation:
- The first pipe fills 1/10th of the tank in one hour. (Rate: 1/10)
- The second pipe fills 1/12th of the tank in one hour. (Rate: 1/12)
- The third pipe empties 1/20th of the tank in one hour. (Rate: -1/20)
- When all three pipes operate simultaneously, the net filling rate of the tank is the sum of the individual rates.
Net filling rate = (1/10) + (1/12) + (-1/20)
= 1/10 + 1/12 - 1/20
= 12/120 + 10/120 - 6/120
= 16/120
= 4/30
= 2/15
- The net filling rate of the tank is 2/15th of the tank per hour.
- To find the time taken to fill the tank completely, we need to divide the tank's capacity (1 unit) by the net filling rate.
Time taken = (Tank capacity)/(Net filling rate)
= 1 / (2/15)
= 15/2
= 7.5 hours
= 7 hours and 30 minutes
Answer:
Therefore, when all three pipes operate simultaneously, the tank will be filled in 7 hours and 30 minutes.
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Two pipes can fill a tank in 10 hours and 12 hours respectively, while a third pipe empties the full tank in 20 hours. If all the three pipes operate simultaneously, in how much time the tank will be filled?a)7 hrsb)8 hrsc)7 hrs. 30 min.d)8 hrs. 30 min.Correct answer is option 'C'. Can you explain this answer?
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