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31 Jul 2024, 09:00
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B
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Difficulty:
65%
(hard)
Question Stats:
59% (02:08) correct
41%
(02:02)
wrong
based on 156
sessions
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A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%. What’s the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
A. 1:3
B. 1:2
C. 2:3
D. 2:1
E. 3:1
A. 1:3
B. 1:2
C. 2:3
D. 2:1
E. 3:1
01 Aug 2024, 18:52
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Lets call the original mixture "A" and the new mixture "B".
A = 40%
B = 25%
Average = 35%
Lets calculate the current weights of A and B to find the average:
25 -------------------35 ----------40
calculating the difference between the end points (A and B) and our average we see that the weights are in the proportion of: 10:5
Going a step further now is determining which of A or B is 10 units and which is 5, we can see that the average is closer to A then B. This means that A is a higher weight than B in the mixture. So we can conclude that Wa:Wb = 10:5
At this point we can use some logic and conclude that our new mixture has 10/15 units of the old mixture. This means that 5/10 units were replaced and changed with the new one.
If we see that the question is asking us for the ratio of "Amount replaced" : "Amount not replaced" = we can fil this in with the information gathered from the point above and see that the solution is 10:5 ----> 2:1 ----- Answer B
Thanks
A = 40%
B = 25%
Average = 35%
Lets calculate the current weights of A and B to find the average:
25 -------------------35 ----------40
calculating the difference between the end points (A and B) and our average we see that the weights are in the proportion of: 10:5
Going a step further now is determining which of A or B is 10 units and which is 5, we can see that the average is closer to A then B. This means that A is a higher weight than B in the mixture. So we can conclude that Wa:Wb = 10:5
At this point we can use some logic and conclude that our new mixture has 10/15 units of the old mixture. This means that 5/10 units were replaced and changed with the new one.
If we see that the question is asking us for the ratio of "Amount replaced" : "Amount not replaced" = we can fil this in with the information gathered from the point above and see that the solution is 10:5 ----> 2:1 ----- Answer B
Thanks
05 Aug 2024, 07:58
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Assume any amount of solution in liters, kg, pounds or whatever. Say equal to 100 for instance.
What you have is 100 liters at 40% concentration --> 40 liters out of 100
you need to take out x liters of 40% solution and replace them with x liters of 25% solution to get the same amount of liters you had (i.e. 100) but at 35% concentration --> 35 liters out of 100
40 - 0.4x + 0.25x = 35 --> x = 1/3 = amount replaced
amount replaced/amount not replaced = (1/3)/(2/3) = 1/2
IMO B
or
0.4 - 0.4x + 0.25x = 0.35 --> x = 1/3 = amount replaced
amount replaced/amount not replaced = (1/3)/(2/3) = 1/2
What you have is 100 liters at 40% concentration --> 40 liters out of 100
you need to take out x liters of 40% solution and replace them with x liters of 25% solution to get the same amount of liters you had (i.e. 100) but at 35% concentration --> 35 liters out of 100
40 - 0.4x + 0.25x = 35 --> x = 1/3 = amount replaced
amount replaced/amount not replaced = (1/3)/(2/3) = 1/2
IMO B
or
0.4 - 0.4x + 0.25x = 0.35 --> x = 1/3 = amount replaced
amount replaced/amount not replaced = (1/3)/(2/3) = 1/2
