A milkman mixes some volume of water to pure milk and gets water milk ...
Solution:
Part 1: Calculation of the amount of water added
Let's assume that the milkman added 'x' litres of water to pure milk to obtain the water milk mixture of 65 litres.
Therefore, the quantity of milk in the mixture will be (65 - x) litres.
Part 2: Calculation of the selling price of the mixture
The milkman sells this solution at a price that is 20% higher per litre than that of pure milk.
Let's assume that the selling price of pure milk is Rs. 'y' per litre.
Therefore, the selling price of the water milk mixture will be Rs. 1.2y per litre.
Part 3: Calculation of the cost price of the mixture
Since the milkman made an overall profit of 50% in this process, it means that the cost price of the water milk mixture is 2/3rd of the selling price.
Therefore, the cost price of the water milk mixture will be (2/3) * 1.2y = 0.8y per litre.
Part 4: Calculation of the amount of water added to 130 litres of pure milk
Now, the milkman mixes the same volume of water to 130 litres of pure milk.
Let's assume that he added 'a' litres of water.
Therefore, the quantity of milk in the mixture will be (130 - a) litres.
Part 5: Calculation of the selling price of the mixture
The milkman sells this solution at a price that is 10% lower than that of pure milk.
Therefore, the selling price of the mixture will be 0.9y per litre.
Part 6: Calculation of the cost price of the mixture
Let's calculate the cost price of the mixture.
The cost price of the mixture will be (130/(130+a)) * 0.8y + (a/(130+a)) * 0 = 104y/(130+a)
Part 7: Calculation of the profit/loss percentage
Profit percentage = ((Selling price - Cost price)/Cost price) * 100
Profit percentage = ((0.9y - 104y/(130+a))/104y/(130+a)) * 100
Profit percentage = ((117 - 10a)/(13a + 169)) * 100
Therefore, the milkman's resultant percentage profit/loss will depend on the value of 'a'.
If 'a' is such that the milkman makes a profit, then the profit percentage will be ((117 - 10a)/(13a + 169)) * 100.
If 'a' is such that the milkman makes a loss, then the loss percentage will be ((117 - 10a)/(13a + 169)) * 100.
Hence, the milkman's profit/loss percentage cannot be determined without knowing the value of 'a'.
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