Understanding the True Gain: How a Milkman Tricks Customers with Water Adulteration

Have you ever wondered how clever business practices can trick customers without them noticing? One such practice, often employed by unscrupulous milk sellers, involves adulterating milk with water to increase profit margins. This article delves into a specific scenario where a milkman sells milk at the cost price but mixes water in it, ultimately gaining 9.09% in profit. We will explore the mathematical reasoning behind this practice and how to calculate the quantity of water added to adhere to the gained profit.

Mathematical Insight: The Gain and Its Implications

Understanding the gain of 9.09% is crucial. This means that for every 100 units of cost price, the milkman sells the mixture for 109.09 units. In terms of volume, this translates to selling 110% of what the cost price represents, effectively getting the price for 1.1 liters of milk for what he actually uses in 1 liter.

Mixing Milk and Water for Profit

Let's denote:

The quantity of milk in the mixture as x liters. The quantity of water added as 1 - x liters. The total volume of the mixture as 1 liter.

If the cost of 1 liter of pure milk is C, then (1 - x) * C represents the cost of the water mixed with the milk. The milkman, however, sells this mixture as 1 liter of pure milk, but because he's using a 0.8-liter measure to pass off 1 liter, he effectively gains 25%. This means 1 - x 0.8, allowing us to solve for x.

Solving the Equation: Calculating the Quantity of Water

The equation can be set up as follows:

1 - x 0.8

Solving for x gives:

x 0.2

This means:

1 - x 1 - 0.2 0.8 liters of water.

To verify this using another method, we can use the given solution:

If we let x be the quantity of water, and 1-x be the quantity of milk, the cost of the mixture can be represented as:

1 - x) * C 0.8 * 1.25 * C

This simplifies to:

1 - x 0.8 * 1.25 1 - 0.893 0.107

Hence, the quantity of water in the mixture of 1 liter is approximately 0.107 liters or 107 milliliters.

Implications and Calculation

The true gain of 9.09% is achieved by the milkman by adding a precise amount of water to the milk. This can be further illustrated by another example where a 12% gain is calculated as follows:

By false weight, the gain is calculated as:

1000 - 800 / 800 25%

If we solve for the quantity of water added, we get:

25x25x / 100 40%

This results in:

x 12

Thus, the amount of water mixed in 1 liter of milk is approximately 12/112 10.71%.

Conclusion

The practice of adulterating milk with water is a common unethical business practice. By understanding the mathematics behind these gains, customers and regulatory bodies can better protect themselves and monitor such practices. The key learning from this example is the importance of careful calculation and transparency in business practices.