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In a solution of common salt in water, the ratio of salt to water was 30:70 as per weight. If we evaporate 100 grams of water from one kilogram of this solution, what will be the ratio of the salt to water by weight?
- a)2:1
- b)1:2
- c)1:3
- d)3:1
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a solution of common salt in water, the ratio of salt to water was ...
Salt = 300 g
Water = 700g
New condition = 300 : 600
= 1 : 2
Water = 700g
New condition = 300 : 600
= 1 : 2
Most Upvoted Answer
In a solution of common salt in water, the ratio of salt to water was ...
Given:
- Ratio of salt to water in the solution = 30:70 (by weight)
- 100 grams of water is evaporated from 1 kilogram of the solution
To find:
The ratio of salt to water by weight after evaporation
Solution:
Step 1: Calculate the initial amounts of salt and water in the solution.
Let's assume the weight of the salt in the solution is '30x' grams and the weight of the water is '70x' grams.
According to the given ratio, the weight of the salt to water is 30x:70x.
Step 2: Calculate the weight of the solution.
The total weight of the solution is the sum of the weights of the salt and water.
Total weight = weight of salt + weight of water
Total weight = 30x + 70x = 100x grams
Step 3: Calculate the weight of the solution after evaporation.
Since 100 grams of water is evaporated, the weight of the solution after evaporation will be reduced by 100 grams.
Weight of the solution after evaporation = Total weight - Weight of evaporated water
Weight of the solution after evaporation = 100x - 100 grams
Step 4: Calculate the new ratio of salt to water after evaporation.
The weight of the salt after evaporation remains the same (30x grams) because only water is evaporated, not the salt.
The weight of the water after evaporation is reduced by 100 grams.
Weight of the water after evaporation = Weight of water - Weight of evaporated water
Weight of the water after evaporation = 70x - 100 grams
The new ratio of salt to water after evaporation = 30x : (70x - 100)
Step 5: Simplify the ratio.
To simplify the ratio, we can divide both sides of the ratio by the highest common factor of 30x and (70x - 100).
Highest common factor of 30x and (70x - 100) is 10.
Simplifying the ratio, we get:
New ratio = 3x : (7x - 10)
Step 6: Substitute the value of x.
To determine the exact ratio, we need the value of x. However, the question does not provide any specific value for x. Therefore, we cannot determine the exact ratio.
However, we can still compare the options given in the question and find the closest match.
Option (B): 1:2
Comparing the option with the simplified ratio, we can see that the simplified ratio has a numerator of 3x, which is approximately double the denominator (7x - 10). Therefore, option (B) is the closest match.
Therefore, the ratio of salt to water by weight after evaporation is approximately 1:2.
- Ratio of salt to water in the solution = 30:70 (by weight)
- 100 grams of water is evaporated from 1 kilogram of the solution
To find:
The ratio of salt to water by weight after evaporation
Solution:
Step 1: Calculate the initial amounts of salt and water in the solution.
Let's assume the weight of the salt in the solution is '30x' grams and the weight of the water is '70x' grams.
According to the given ratio, the weight of the salt to water is 30x:70x.
Step 2: Calculate the weight of the solution.
The total weight of the solution is the sum of the weights of the salt and water.
Total weight = weight of salt + weight of water
Total weight = 30x + 70x = 100x grams
Step 3: Calculate the weight of the solution after evaporation.
Since 100 grams of water is evaporated, the weight of the solution after evaporation will be reduced by 100 grams.
Weight of the solution after evaporation = Total weight - Weight of evaporated water
Weight of the solution after evaporation = 100x - 100 grams
Step 4: Calculate the new ratio of salt to water after evaporation.
The weight of the salt after evaporation remains the same (30x grams) because only water is evaporated, not the salt.
The weight of the water after evaporation is reduced by 100 grams.
Weight of the water after evaporation = Weight of water - Weight of evaporated water
Weight of the water after evaporation = 70x - 100 grams
The new ratio of salt to water after evaporation = 30x : (70x - 100)
Step 5: Simplify the ratio.
To simplify the ratio, we can divide both sides of the ratio by the highest common factor of 30x and (70x - 100).
Highest common factor of 30x and (70x - 100) is 10.
Simplifying the ratio, we get:
New ratio = 3x : (7x - 10)
Step 6: Substitute the value of x.
To determine the exact ratio, we need the value of x. However, the question does not provide any specific value for x. Therefore, we cannot determine the exact ratio.
However, we can still compare the options given in the question and find the closest match.
Option (B): 1:2
Comparing the option with the simplified ratio, we can see that the simplified ratio has a numerator of 3x, which is approximately double the denominator (7x - 10). Therefore, option (B) is the closest match.
Therefore, the ratio of salt to water by weight after evaporation is approximately 1:2.
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In a solution of common salt in water, the ratio of salt to water was 30:70 as per weight. If we evaporate 100 grams of water from one kilogram of this solution, what will be the ratio of the salt to water by weight?a)2:1b)1:2c)1:3d)3:1Correct answer is option 'B'. Can you explain this answer?
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