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14 Jul 2023, 01:02
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (02:34) correct
37%
(02:21)
wrong
based on 231
sessions
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The radiator of an automobile is filled to capacity with 8 liters of a solution that is 20% liquid x. The automobile engine overheats, and 6 liters of water evaporate, leaving 2 liters of concentrated liquid x solution If the radiator is refilled with 6 liters of a solution that is 20% liquid x, what will be the concentration of the resulting solution?
A. 20%
B. 25%
C. 30%
D. 35%
E. 40%
A. 20%
B. 25%
C. 30%
D. 35%
E. 40%
14 Jul 2023, 01:41
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The radiator of an automobile is filled to capacity with 8 liters of a solution that is 20% liquid x. The automobile engine overheats, and 6 liters of water evaporate, leaving 2 liters of concentrated liquid x solution If the radiator is refilled with 6 liters of a solution that is 20% liquid x, what will be the concentration of the resulting solution ?
Assuming that the solution contains only liquid X and water.
Lets solve this in a step wise fashion :
step 1: radiator is filled with 8 liter solution which is 20% x.
So x = 0.2* 8 = 1.6 liters, following this water = 8 -1.6 liter = 6.4 liters.
step 2: 6 liters of water is evaporate.
so what we have left is :
x = 1.6 liter and water = 0.4 liter
totaling to 2 liters of solution.
step 3 : 6 liters of 20% solution x is added.
In the 6 liters of the above mentioned solution, we have 1.2 liter X and 4.8 liter water.
Adding it to the solution obtained from step 2 we have :
2.8 liter x and 5.2 liter water solution.
totaling to 8 liter of solution.
step 4: calculate the percentage of X
\(\frac{2.8}{8 }* 100 = 7 * 5 = 35\)%
Hence IMO option D.
Assuming that the solution contains only liquid X and water.
Lets solve this in a step wise fashion :
step 1: radiator is filled with 8 liter solution which is 20% x.
So x = 0.2* 8 = 1.6 liters, following this water = 8 -1.6 liter = 6.4 liters.
step 2: 6 liters of water is evaporate.
so what we have left is :
x = 1.6 liter and water = 0.4 liter
totaling to 2 liters of solution.
step 3 : 6 liters of 20% solution x is added.
In the 6 liters of the above mentioned solution, we have 1.2 liter X and 4.8 liter water.
Adding it to the solution obtained from step 2 we have :
2.8 liter x and 5.2 liter water solution.
totaling to 8 liter of solution.
step 4: calculate the percentage of X
\(\frac{2.8}{8 }* 100 = 7 * 5 = 35\)%
Hence IMO option D.
10 Aug 2023, 10:03
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Bunuel
Solution:
- Initial condition: 8 liter solution
- Liquid \(x = 20\%\) of \(8 = 1.6\) liters
- Water \(= 8 - 1.6 = 6.4\) liters
- After overheating:
- Liquid \(x = 1.6\) liters (same)
- Water \(= 6.4-6=0.4\) liters
- Concentration \(=\frac{1.6}{1.6+0.4} \times 100=80\%\) liquid x
- So, we are basically mixing 2 liters of 80% liquid x solution with 6 liters of 20% liquid x solution
- If we assume the resultant concentration be \(a\), then we can form an equation \(\frac{a-20}{80-a}=\frac{2}{6}\)
- And we will get \(a=35\%\) concentration
Hence the right answer is Option D
