Milkman Profit Calculation with Water Mixture
This solution explains how to calculate the profit percentage when a milkman mixes water into pure milk twice and sells the mixture at the cost price.
Problem Analysis
- A milkman adds 10% water initially.
- He then adds another 10% water based on the previous mixture's volume.
- The final mixture is sold at the cost price of the original pure milk.
Step-by-Step Solution
Step 1: Assume Initial Quantity and Cost
Let's assume the initial quantity of pure milk is 100 units.
Let the cost price of 1 unit of pure milk be $C.
Therefore, the initial Cost Price (CP) of the milk is:
$ \text{CP} = 100 \text{ units} \times C/\text{unit} = 100C $
Step 2: Calculate Mixture Volume after First Water Addition
The milkman first mixes 10% water in pure milk.
Water added = $ 10\% \times 100 \text{ units} = 10 \text{ units} $.
The new volume of the mixture after the first addition is:
$ \text{Volume}_1 = 100 \text{ units} (\text{milk}) + 10 \text{ units} (\text{water}) = 110 \text{ units} $
Step 3: Calculate Final Mixture Volume after Second Water Addition
He then adds 10% more water based on the previous mixture's volume (110 units).
Additional water added = $ 10\% \times 110 \text{ units} = 11 \text{ units} $.
The final volume of the mixture is:
$ \text{Final Volume} = \text{Volume}_1 + \text{Additional Water} = 110 \text{ units} + 11 \text{ units} = 121 \text{ units} $
Step 4: Determine Selling Price (SP)
The milkman sells the final mixture (121 units) at the cost price. This implies the selling price per unit volume is the same as the cost price per unit volume of pure milk ($C$).
Total Selling Price (SP) = $ \text{Final Volume} \times C/\text{unit} $
$ \text{SP} = 121 \text{ units} \times C/\text{unit} = 121C $
Step 5: Calculate Profit
Profit is the difference between the Selling Price and the Cost Price.
$ \text{Profit} = \text{SP} - \text{CP} $
$ \text{Profit} = 121C - 100C = 21C $
Step 6: Calculate Profit Percentage
The profit percentage is calculated based on the initial Cost Price.
$ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 $
$ \text{Profit Percentage} = \left( \frac{21C}{100C} \right) \times 100 $
$ \text{Profit Percentage} = \frac{21}{100} \times 100 = 21\% $
Conclusion
By adding water twice, the milkman increases the volume. When this larger volume is sold at the original cost price per unit, it results in a significant profit.
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Important Questions from Mixture and Alligation
My father is presently 25 years older than me. The sum of our ages 5 years ago was 39 years. Find my present age.
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If a + b + c = 0, then the value of (a² + b² + 2ab) is equal to:
