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A solution contains water, milk and liquid chocolate in the ratio of 2:3:5 by volume. If y liters of water and milk each are added to this solution, the resultant solution would contain 25 percent of water by volume. If the volume of this resultant solution is 120 liters, what is the value of y in liters?
- a)8
- b)10
- c)11
- d)12
- e)15
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A solution contains water, milk and liquid chocolate in the ratio of 2...
Given:
- Ratio of water, milk and liquid chocolate in the original solution is 2:3:5
- Let the volume of water, milk and liquid chocolate in the original solution be 2x, 3x and 5x respectively
- Total volume of the original solution= 2x+3x+5x = = 10x
- Water added to the original solution= y liters
- Milk added to the original solution= y liters
- Total volume of the resultant solution = 120 liters
- Volume of water in the resultant solution = 25% of the total volume
- So, Volume of water in the resultant solution= 25% of 120 = 30 liters
To Find: Value of y?
Approach :
- We will first find the volume of water in the resultant solution after addition of water to the original solution. This will give us one equation in x and y.
a. Volume of water in the original solution =2x liters
b. Volume of water added to the original solution =y liters
c. So, Volume of water in the resultant solution = (2x+y) liters
d. The total volume of water in the new solution is also equal to 30 liters.
b. Volume of water added to the original solution =y liters
c. So, Volume of water in the resultant solution = (2x+y) liters
d. The total volume of water in the new solution is also equal to 30 liters.
- So,we have,2x + y = 30 (Equation 1).
2. We will then find the total volume of the resultant solution to get another equation in x and y.
- Volume of water in the resultant solution = 2x+y (Already established above)
- Volume of milk in the resultant solution = 3x+y (3x liters milk in original solution added to y liters of milk solution)
- Volume of liquid chocolate in the resultant solution =5x liters (No liquid chocolate is added)
- So, total volume of the resultant solution = (2x+y)+(3x+y)+(5x) =10x+2y liters
- The total volume of solution is also equal to 120 liters.
- So, we have, 10x+2y=120 (Equation 2)
3. Using the two equations in x nd y, we will be able to find the value of y as asked in the question.
Working out:
- From equation 1, we have 2x + y = 30
- From equation 2, we have 10x+2y=120
- Solving equation 1 and 2
- Performing (Equation 1) *5, we get 10x+5y =150 (Equation 3)
- Doing (Equation 3) – (Equation 2), we get
- (10x+5y)-(10x+2y)=150-120
- 3y=30
- y=10 liters
4. So water to be added to the original solution is 10 liters.
5. So answer option B is correct.
5. So answer option B is correct.
Most Upvoted Answer
A solution contains water, milk and liquid chocolate in the ratio of 2...
Understanding the Initial Solution
- The initial volume ratio of water, milk, and liquid chocolate is 2:3:5.
- Total parts = 2 + 3 + 5 = 10 parts.
- Let the total initial volume be V liters. Then:
- Water = (2/10)V = 0.2V
- Milk = (3/10)V = 0.3V
- Chocolate = (5/10)V = 0.5V
Adding Water and Milk
- Let y liters of water and y liters of milk be added.
- New volume of water = 0.2V + y
- New volume of milk = 0.3V + y
- Volume of chocolate remains = 0.5V
Resultant Volume and Composition
- The resultant volume of the solution = 0.2V + 0.3V + 0.5V + y + y = V + 2y.
- Given that the resultant solution is 120 liters:
- V + 2y = 120
Water Percentage Calculation
- The resultant percentage of water is given as 25%:
- (Water Volume / Total Volume) * 100 = 25
- (0.2V + y) / (V + 2y) = 0.25
Setting Up the Equations
1. From the volume equation:
- V = 120 - 2y
2. Substitute V in the percentage equation:
- (0.2(120 - 2y) + y) / (120) = 0.25
- (24 - 0.4y + y) = 30
- 0.6y = 6
- y = 10
Conclusion
- The value of y is 10 liters, confirming that the correct answer is option 'B'.
- The initial volume ratio of water, milk, and liquid chocolate is 2:3:5.
- Total parts = 2 + 3 + 5 = 10 parts.
- Let the total initial volume be V liters. Then:
- Water = (2/10)V = 0.2V
- Milk = (3/10)V = 0.3V
- Chocolate = (5/10)V = 0.5V
Adding Water and Milk
- Let y liters of water and y liters of milk be added.
- New volume of water = 0.2V + y
- New volume of milk = 0.3V + y
- Volume of chocolate remains = 0.5V
Resultant Volume and Composition
- The resultant volume of the solution = 0.2V + 0.3V + 0.5V + y + y = V + 2y.
- Given that the resultant solution is 120 liters:
- V + 2y = 120
Water Percentage Calculation
- The resultant percentage of water is given as 25%:
- (Water Volume / Total Volume) * 100 = 25
- (0.2V + y) / (V + 2y) = 0.25
Setting Up the Equations
1. From the volume equation:
- V = 120 - 2y
2. Substitute V in the percentage equation:
- (0.2(120 - 2y) + y) / (120) = 0.25
- (24 - 0.4y + y) = 30
- 0.6y = 6
- y = 10
Conclusion
- The value of y is 10 liters, confirming that the correct answer is option 'B'.
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A solution contains water, milk and liquid chocolate in the ratio of 2:3:5 by volume. If y liters of water and milk each are added to this solution, the resultant solution would contain 25 percent of water by volume. If the volume of this resultant solution is 120 liters, what is the value of y in liters?a)8b)10c)11d)12e)15Correct answer is option 'B'. Can you explain this answer?
Question Description
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