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26 May 2017, 04:48
Kudos
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The 20kg mixture comprised of water and sand is mixed evenly so that the ratio of water to sand is 8 to 2. If part of the mixture is replaced by sand to make the ratio of water to sand as 6 to 4, what is the amount of mixture replaced by sand, in kg?
A. 4.0
B. 5.0
C. 6.8
D. 7.6
E. 8.4
A. 4.0
B. 5.0
C. 6.8
D. 7.6
E. 8.4
26 May 2017, 04:49
Kudos
Bookmarks
Official Solution:
The 20kg mixture comprised of water and sand is mixed evenly so that the ratio of water to sand is 8 to 2. If part of the mixture is replaced by sand to make the ratio of water to sand as 6 to 4, what is the amount of mixture replaced by sand, in kg?
A. 4.0
B. 5.0
C. 6.8
D. 7.6
E. 8.4
If the mixture comprised of water and sand weighs 20kg in total and the ratio of water to sand is \(8:2\), there should be 16kg of water and 4 kg of sand as shown in the diagram below. However, in order for the ratio to be changed to \(6:4\), 4kg of water shaded should be taken out, but since the mixture is mixed evenly, \(0.5kg+0.5kg = 1kg\) of sand is also taken out at the same time.
If so, the amount of the mixture that has been taken out is \(4kg + 1kg = 5kg\), and if this is all replaced with sand, the ratio of water to sand is \((16kg-4kg):(4kg-1kg+5kg) = 12kg:8kg = 6:4\). Therefore, the answer is B.
Answer: B
The 20kg mixture comprised of water and sand is mixed evenly so that the ratio of water to sand is 8 to 2. If part of the mixture is replaced by sand to make the ratio of water to sand as 6 to 4, what is the amount of mixture replaced by sand, in kg?
A. 4.0
B. 5.0
C. 6.8
D. 7.6
E. 8.4
If the mixture comprised of water and sand weighs 20kg in total and the ratio of water to sand is \(8:2\), there should be 16kg of water and 4 kg of sand as shown in the diagram below. However, in order for the ratio to be changed to \(6:4\), 4kg of water shaded should be taken out, but since the mixture is mixed evenly, \(0.5kg+0.5kg = 1kg\) of sand is also taken out at the same time.
If so, the amount of the mixture that has been taken out is \(4kg + 1kg = 5kg\), and if this is all replaced with sand, the ratio of water to sand is \((16kg-4kg):(4kg-1kg+5kg) = 12kg:8kg = 6:4\). Therefore, the answer is B.
Answer: B
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