Question
- A milkman purchases pure milk at Rs 3.00 per litre and makes a profit of 12\(\frac{1}{2}\)% by adulterating the milk with water and selling the mixture at Rs 3.15 per litre. What is the ratio of milk to water that his customers receive?
Answer: Option D
Let us assume that the milkman initially purchases x liters of pure milk at Rs. 3.00 per litre.
After adulterating the milk with water, he sells the mixture at Rs. 3.15 per litre, making a profit of 12%.
We need to find the ratio of milk to water in the final mixture.
Let us suppose that the milkman adds y liters of water to x liters of pure milk to make the final mixture.
The cost price of x liters of pure milk is Rs. 3x.
The cost of y liters of water is zero as it is freely available.
The total cost of the final mixture is the sum of the cost of milk and the cost of water, which is Rs. 3x + 0 = Rs. 3x.
Since the milkman sells the mixture at Rs. 3.15 per litre, his selling price for x + y litres of the mixture is Rs. 3.15(x + y).
Profit% = [(Selling price - Cost price) / Cost price] × 100
We are given that the milkman makes a profit of 12% by selling the mixture.
Therefore, [(3.15(x + y) - 3x) / 3x] × 100 = 12
Simplifying this equation, we get:
y/x = 4/5
This means that for every 4 units of water, the milkman adds 5 units of pure milk to make the final mixture.
Therefore, the ratio of milk to water in the final mixture is 5:4.
Hence, the correct answer is option D none of these.
To summarize the solution steps:
Let x be the quantity of pure milk purchased by the milkman at Rs. 3.00 per litre.Let y be the quantity of water added to the milk to make the final mixture.Cost price of the final mixture is Rs. 3x.Selling price of the final mixture is Rs. 3.15(x + y).Profit% = 12%.Simplify the profit% equation to get y/x = 4/5.The ratio of milk to water in the final mixture is 5:4.If you think the solution is wrong then please provide your own solution below in the comments section .
Was this answer helpful ?
Let us assume that the milkman initially purchases x liters of pure milk at Rs. 3.00 per litre.
After adulterating the milk with water, he sells the mixture at Rs. 3.15 per litre, making a profit of 12%.
We need to find the ratio of milk to water in the final mixture.
Let us suppose that the milkman adds y liters of water to x liters of pure milk to make the final mixture.
The cost price of x liters of pure milk is Rs. 3x.
The cost of y liters of water is zero as it is freely available.
The total cost of the final mixture is the sum of the cost of milk and the cost of water, which is Rs. 3x + 0 = Rs. 3x.
Since the milkman sells the mixture at Rs. 3.15 per litre, his selling price for x + y litres of the mixture is Rs. 3.15(x + y).
Profit% = [(Selling price - Cost price) / Cost price] × 100
We are given that the milkman makes a profit of 12% by selling the mixture.
Therefore, [(3.15(x + y) - 3x) / 3x] × 100 = 12
Simplifying this equation, we get:
y/x = 4/5
This means that for every 4 units of water, the milkman adds 5 units of pure milk to make the final mixture.
Therefore, the ratio of milk to water in the final mixture is 5:4.
Hence, the correct answer is option D none of these.
To summarize the solution steps:
Let x be the quantity of pure milk purchased by the milkman at Rs. 3.00 per litre.Let y be the quantity of water added to the milk to make the final mixture.Cost price of the final mixture is Rs. 3x.Selling price of the final mixture is Rs. 3.15(x + y).Profit% = 12%.Simplify the profit% equation to get y/x = 4/5.The ratio of milk to water in the final mixture is 5:4.If you think the solution is wrong then please provide your own solution below in the comments section .
Was this answer helpful ?
More Questions on This Topic :
Latest Videos
Latest Test Papers
Submit Solution