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A vessel contains 60 liters mixture of milk and water in a ratio 5 : 1 respectively. What quantity of the mixture must be replaced with water so the ratio of the milk to water in the resultant mixture becomes 1 : 1?
- a)20 liters
- b)24 liters
- c)25 liters
- d)30 liters
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A vessel contains 60 liters mixture of milk and water in a ratio 5 : 1...
Removed milk = 50 – 30 = 20
Hence, option B is correct.
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A vessel contains 60 liters mixture of milk and water in a ratio 5 : 1...
Given Information:
- The vessel contains a mixture of milk and water in a ratio of 5:1.
- The total quantity of the mixture in the vessel is 60 liters.
Objective:
To determine the quantity of the mixture that must be replaced with water so that the ratio of milk to water becomes 1:1.
Solution:
Let's assume that x liters of the mixture is to be replaced with water.
Step 1: Determining the initial quantities of milk and water
- The initial ratio of milk to water in the vessel is 5:1, so we can calculate the initial quantities of milk and water as follows:
- Quantity of milk = (5/6) * 60 liters (since the total ratio is 5+1=6)
- Quantity of water = (1/6) * 60 liters
Step 2: Determining the final quantities of milk and water
- After replacing x liters of the mixture with water, the ratio of milk to water becomes 1:1.
- So, the quantity of milk and water in the vessel will be equal.
- Let's assume the final quantity of milk and water in the vessel is y liters each.
- Therefore, the final quantities of milk and water can be calculated as follows:
- Quantity of milk = y liters
- Quantity of water = y liters
Step 3: Setting up the equation
- The equation can be set up based on the quantities of milk and water.
- The equation can be written as:
- Quantity of milk / Quantity of water = Initial quantity of milk / Initial quantity of water
Step 4: Solving the equation
- Substituting the initial and final quantities of milk and water into the equation, we get:
- (5/6) * 60 / (1/6) * 60 = y / y
- 5 = 1
- This equation is not true, which means our assumption is incorrect.
- Therefore, there is no possible value of x that can satisfy the condition of the problem.
Conclusion:
Based on our calculations, there is no quantity of the mixture that can be replaced with water so that the ratio of milk to water becomes 1:1. Therefore, the correct answer should be "None of the above" as none of the given options is valid.
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A vessel contains 60 liters mixture of milk and water in a ratio 5 : 1 respectively. What quantity of the mixture must be replaced with water so the ratio of the milk to water in the resultant mixture becomes 1 : 1?a)20 litersb)24 litersc)25 litersd)30 litersCorrect answer is option 'B'. Can you explain this answer?
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