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Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
- a)6/11
- b)5/11
- c)8/11
- d)7/11
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Three pipes A, B and C can fill a tank from empty to full in 30 minute...
Part of the tank filled by pipe A in 1 minute =1/30
Part of the tank filled by pipe B in 1 minute =1/20
Part of the tank filled by pipe C in 1 minute =1/10
Here we have to find the proportion of the solution R.
Pipe C discharges chemical solution R.
Part of the tank filled by pipe B in 1 minute =1/20
Part of the tank filled by pipe C in 1 minute =1/10
Here we have to find the proportion of the solution R.
Pipe C discharges chemical solution R.
Most Upvoted Answer
Three pipes A, B and C can fill a tank from empty to full in 30 minute...
Understanding the Problem
We have three pipes A, B, and C that fill a tank in different times:
- Pipe A fills the tank in 30 minutes.
- Pipe B fills the tank in 20 minutes.
- Pipe C fills the tank in 10 minutes.
When all pipes are opened simultaneously, we need to find the proportion of solution R (from pipe C) in the tank after 3 minutes.
Calculating Individual Filling Rates
- Pipe A's rate: 1 tank in 30 minutes = 1/30 tank/minute
- Pipe B's rate: 1 tank in 20 minutes = 1/20 tank/minute
- Pipe C's rate: 1 tank in 10 minutes = 1/10 tank/minute
Total Rate of Filling
The total rate of filling when all pipes are open is:
- Total rate = (1/30 + 1/20 + 1/10) tank/minute
Finding a common denominator (60):
- Total rate = (2/60 + 3/60 + 6/60) = 11/60 tank/minute
Amount Filled in 3 Minutes
In 3 minutes, the amount of tank filled is:
- Amount filled = Total rate × Time = (11/60) × 3 = 11/20 tank
Calculating Proportion of Each Solution
Next, we calculate the contribution from each pipe in 3 minutes:
- From Pipe A: (1/30) × 3 = 1/10 tank
- From Pipe B: (1/20) × 3 = 3/20 tank
- From Pipe C: (1/10) × 3 = 3/10 tank
Now converting all contributions to a common denominator of 20:
- Pipe A: 2/20
- Pipe B: 3/20
- Pipe C: 6/20
Total Contribution from Pipe C
The total contributions add up to:
- Total filled = 2/20 + 3/20 + 6/20 = 11/20 tank
Proportion of Solution R
Finally, the proportion of solution R from Pipe C in the total liquid is:
- Proportion of R = (Amount from C) / (Total filled) = (6/20) / (11/20) = 6/11
Thus, the correct answer is option A) 6/11.
We have three pipes A, B, and C that fill a tank in different times:
- Pipe A fills the tank in 30 minutes.
- Pipe B fills the tank in 20 minutes.
- Pipe C fills the tank in 10 minutes.
When all pipes are opened simultaneously, we need to find the proportion of solution R (from pipe C) in the tank after 3 minutes.
Calculating Individual Filling Rates
- Pipe A's rate: 1 tank in 30 minutes = 1/30 tank/minute
- Pipe B's rate: 1 tank in 20 minutes = 1/20 tank/minute
- Pipe C's rate: 1 tank in 10 minutes = 1/10 tank/minute
Total Rate of Filling
The total rate of filling when all pipes are open is:
- Total rate = (1/30 + 1/20 + 1/10) tank/minute
Finding a common denominator (60):
- Total rate = (2/60 + 3/60 + 6/60) = 11/60 tank/minute
Amount Filled in 3 Minutes
In 3 minutes, the amount of tank filled is:
- Amount filled = Total rate × Time = (11/60) × 3 = 11/20 tank
Calculating Proportion of Each Solution
Next, we calculate the contribution from each pipe in 3 minutes:
- From Pipe A: (1/30) × 3 = 1/10 tank
- From Pipe B: (1/20) × 3 = 3/20 tank
- From Pipe C: (1/10) × 3 = 3/10 tank
Now converting all contributions to a common denominator of 20:
- Pipe A: 2/20
- Pipe B: 3/20
- Pipe C: 6/20
Total Contribution from Pipe C
The total contributions add up to:
- Total filled = 2/20 + 3/20 + 6/20 = 11/20 tank
Proportion of Solution R
Finally, the proportion of solution R from Pipe C in the total liquid is:
- Proportion of R = (Amount from C) / (Total filled) = (6/20) / (11/20) = 6/11
Thus, the correct answer is option A) 6/11.
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Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?a)6/11b)5/11c)8/11d)7/11Correct answer is option 'A'. Can you explain this answer?
Question Description
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