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A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
- a)1/3
- b)1/4
- c)1/5
- d)1/6
- e)1/7
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A vessel is filled with liquid, 3 parts of which are water and 5 parts...
Let the quantity of the initial liquid in the vessel = 8 litre and
quantity of water in the initial liquid = 3 litre and
quantity of syrup in the initial liquid = 5 litre
Let x litre of the mixture is drawn off and replaced with waterQuantity of water in the new mixture
Quantity of syrup in the new mixture
Given that in the new mixture, quantity of water = quantity of syrup
Initially we assumed that the quantity of the initial liquid in the vessel = 8 litre for the ease of calculations. For that 8/5 litre of the mixture to be drawn off and replaced with water so that the mixture may be half water and half syrup
Now, if the initial liquid in the vessel = 1 litre, quantity of the mixture to be drawn off and replaced with water so that the mixture may be half water and half syrup
It means 1/5 of the mixture has to be drawn off and replaced with water so that the mixture
quantity of water in the initial liquid = 3 litre and
quantity of syrup in the initial liquid = 5 litre
Let x litre of the mixture is drawn off and replaced with waterQuantity of water in the new mixture
Quantity of syrup in the new mixture
Given that in the new mixture, quantity of water = quantity of syrup
Initially we assumed that the quantity of the initial liquid in the vessel = 8 litre for the ease of calculations. For that 8/5 litre of the mixture to be drawn off and replaced with water so that the mixture may be half water and half syrup
Now, if the initial liquid in the vessel = 1 litre, quantity of the mixture to be drawn off and replaced with water so that the mixture may be half water and half syrup
It means 1/5 of the mixture has to be drawn off and replaced with water so that the mixture
may be half water and half syrup
Most Upvoted Answer
A vessel is filled with liquid, 3 parts of which are water and 5 parts...
Understanding the Problem:
In this problem, we have a vessel filled with a liquid that has 3 parts water and 5 parts syrup. We need to find out how much of the mixture should be drawn off and replaced with water so that the mixture becomes half water and half syrup.
Solution:
Let's assume the total quantity of the mixture in the vessel is 8 units (3 parts water + 5 parts syrup).
Step 1: Drawing off and replacing
- Let x units of the mixture be drawn off and replaced with water.
- After drawing off x units, the quantity of water in the mixture remains 3(8-x)/8 units.
- The quantity of syrup remains 5(8-x)/8 units.
Step 2: Setting up equation
- According to the question, the new mixture is half water and half syrup.
- Therefore, we have the equation:
3(8-x)/8 = 5(8-x)/8
Step 3: Solving the equation
- Solving the above equation, we get x = 5.
- This means 5 units of the mixture must be drawn off and replaced with water.
Therefore, the correct answer is option C) 1/5.
In this problem, we have a vessel filled with a liquid that has 3 parts water and 5 parts syrup. We need to find out how much of the mixture should be drawn off and replaced with water so that the mixture becomes half water and half syrup.
Solution:
Let's assume the total quantity of the mixture in the vessel is 8 units (3 parts water + 5 parts syrup).
Step 1: Drawing off and replacing
- Let x units of the mixture be drawn off and replaced with water.
- After drawing off x units, the quantity of water in the mixture remains 3(8-x)/8 units.
- The quantity of syrup remains 5(8-x)/8 units.
Step 2: Setting up equation
- According to the question, the new mixture is half water and half syrup.
- Therefore, we have the equation:
3(8-x)/8 = 5(8-x)/8
Step 3: Solving the equation
- Solving the above equation, we get x = 5.
- This means 5 units of the mixture must be drawn off and replaced with water.
Therefore, the correct answer is option C) 1/5.
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A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?a)1/3b)1/4c)1/5d)1/6e)1/7Correct answer is option 'C'. Can you explain this answer?
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