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31 Jul 2025, 08:22
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A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?
A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49
A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49
31 Jul 2025, 08:22
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Official Solution:
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?
A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49
Assuming the initial weight of the solution was 100 kg, the amount of salt would be 2% of 100 kg = 2 kg. After some water is added, the amount of salt remains the same. If \(x\) kg of water is added, then 2 kg of salt becomes 1% of \((100 + x)\) kg. So:
\(2 = \frac{1}{100} * (100 + x)\)
\(x = 100\)
Thus, the initial amount of water was 98 kg, and the final amount is 98 + 100 = 198 kg.
The required ratio is 198:98 = 99:49.
Answer: D
A saline solution is 2% salt by weight, with the rest being water. After more water is added, the salt concentration decreases to 1% by weight. What is the ratio of the final weight of water to the initial weight of water in the solution?
A. 1:2
B. 50:49
C. 2:1
D. 99:49
E. 100:49
Assuming the initial weight of the solution was 100 kg, the amount of salt would be 2% of 100 kg = 2 kg. After some water is added, the amount of salt remains the same. If \(x\) kg of water is added, then 2 kg of salt becomes 1% of \((100 + x)\) kg. So:
\(2 = \frac{1}{100} * (100 + x)\)
\(x = 100\)
Thus, the initial amount of water was 98 kg, and the final amount is 98 + 100 = 198 kg.
The required ratio is 198:98 = 99:49.
Answer: D
