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Updated on: 15 Oct 2023, 03:13
Originally posted by arjtryarjtry on 02 Sep 2008, 02:23.
Last edited by Bunuel on 15 Oct 2023, 03:13, edited 2 times in total.
Last edited by Bunuel on 15 Oct 2023, 03:13, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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If both valves are open simultaneously, they can fill an empty pool in 48 minutes. The first valve, when working independently, takes 2 hours to fill the pool. If the second valve releases 50 cubic meters of water more than the first valve every minute, what is the capacity of the pool?
A. 9,000 cubic meters
B. 10,500 cubic meters
C. 11,750 cubic meters
D. 12,000 cubic meters
E. 12,500 cubic meters
M12-10
A. 9,000 cubic meters
B. 10,500 cubic meters
C. 11,750 cubic meters
D. 12,000 cubic meters
E. 12,500 cubic meters
M12-10
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23 Apr 2014, 00:15
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If both valves are open simultaneously, they can fill an empty pool in 48 minutes. The first valve, when working independently, takes 2 hours to fill the pool. If the second valve releases 50 cubic meters of water more than the first valve every minute, what is the capacity of the pool?
A. 9,000 cubic meters
B. 10,500 cubic meters
C. 11,750 cubic meters
D. 12,000 cubic meters
E. 12,500 cubic meters
Let the rate of the first valve be \(x\) cubic meters per minute. The rate of the second valve will then be \(x + 50\) cubic meters per minute.
Given that both valves together fill the pool in 48 minutes, the capacity of the pool can be calculated as \(C = \text{time}*\text{combined rate} = 48 \times (x + x + 50) = 48(2x + 50)\).
Since the first valve alone fills the pool in 2 hours (or 120 minutes), the capacity of the pool can also be represented as \(C = \text{time} *\text{rate} = 120x\).
Equating the two expressions for \(C\), we have \(120x = 48(2x + 50)\). Solving for \(x\), we get \(x = 100\), which implies \(C = 120x = 12,000\) cubic meters.
Answer: D
A. 9,000 cubic meters
B. 10,500 cubic meters
C. 11,750 cubic meters
D. 12,000 cubic meters
E. 12,500 cubic meters
Let the rate of the first valve be \(x\) cubic meters per minute. The rate of the second valve will then be \(x + 50\) cubic meters per minute.
Given that both valves together fill the pool in 48 minutes, the capacity of the pool can be calculated as \(C = \text{time}*\text{combined rate} = 48 \times (x + x + 50) = 48(2x + 50)\).
Since the first valve alone fills the pool in 2 hours (or 120 minutes), the capacity of the pool can also be represented as \(C = \text{time} *\text{rate} = 120x\).
Equating the two expressions for \(C\), we have \(120x = 48(2x + 50)\). Solving for \(x\), we get \(x = 100\), which implies \(C = 120x = 12,000\) cubic meters.
Answer: D
17 May 2016, 21:57
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Responding to a pm:
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?
(A) 9000 cubic meters
(B) 10500 cubic meters
(C) 11750 cubic meters
(D) 12000 cubic meters
(E) 12500 cubic meters
Normally, I would do this question the algebra way (I wouldn't use ratios here because partial data is in time and partial in work form):
Say, capacity of the pool is x cubic meters. Consider time in minutes.
First valve rate = Work/Time = x/120
Second valve rate = x/120 + 50
Combined rate = x/48
x/48 = x/120 + x/120 + 50
x/48 - x/60 = 50
x/4 - x/5 = 12*50
x = 12*50*20 = 12000
But if I am short on time, I can take a guess.
Most probably, the rate of work will be an integer .... cubic meters per minute. The additional rate of valve 2 is 50 cubic meters per minute so it is unlikely that rate of valve 1 will be something like 150.38 cubic meters per min. It will most probably be an integer.
Assuming that, I see that only option (D) is divisible by 48.
(48 has four 2s. 9000 has three 2s, 10500 has two 2s, 11750 has one 2 and 12500 has two 2s)
So most probably answer will be 12000. Let's check.
12000/48 = 250
12000/120 = 100
Valve 1 rate is 100 cubic meters per min. Valve 2 rate is 150 cubic meters per min.
Everything matches.
Answer (D)
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?
(A) 9000 cubic meters
(B) 10500 cubic meters
(C) 11750 cubic meters
(D) 12000 cubic meters
(E) 12500 cubic meters
Normally, I would do this question the algebra way (I wouldn't use ratios here because partial data is in time and partial in work form):
Say, capacity of the pool is x cubic meters. Consider time in minutes.
First valve rate = Work/Time = x/120
Second valve rate = x/120 + 50
Combined rate = x/48
x/48 = x/120 + x/120 + 50
x/48 - x/60 = 50
x/4 - x/5 = 12*50
x = 12*50*20 = 12000
But if I am short on time, I can take a guess.
Most probably, the rate of work will be an integer .... cubic meters per minute. The additional rate of valve 2 is 50 cubic meters per minute so it is unlikely that rate of valve 1 will be something like 150.38 cubic meters per min. It will most probably be an integer.
Assuming that, I see that only option (D) is divisible by 48.
(48 has four 2s. 9000 has three 2s, 10500 has two 2s, 11750 has one 2 and 12500 has two 2s)
So most probably answer will be 12000. Let's check.
12000/48 = 250
12000/120 = 100
Valve 1 rate is 100 cubic meters per min. Valve 2 rate is 150 cubic meters per min.
Everything matches.
Answer (D)
