A milkman mixes water with pure milk. If he sells the mixture at the cost price of pure milk and makes a profit of 25%, what is the ratio of water to milk in the mixture?

The correct option is 1:4.

Step-by-Step Explanation:

Let us assume the cost price (CP) of 1 liter of pure milk is Rs. 1.

Since the milkman sells the mixture at the cost price of pure milk, the selling price (SP) of 1 liter of the mixture is also Rs. 1.

He makes a profit of 25% by mixing water (which is assumed to cost Rs. 0).

Now, let us calculate the cost price (CP) of 1 liter of the mixture using the profit percentage formula:

$\text{CP of 1 liter of mixture}=\frac{\text{SP}}{1+\frac{\text{Profit \%}}{100}}$

Substituting the given values:

$\text{CP of 1 liter of mixture}=\frac{1}{1+\frac{25}{100}}=\frac{1}{1+0.25}=\frac{1}{1.25}=\frac{4}{5}$

This means that in 1 liter of the mixture, the cost of the pure milk present is Rs. 4/5.

Since 1 liter of pure milk costs Rs. 1, the quantity of pure milk in 1 liter of the mixture is:

$\text{Quantity of Milk}=\frac{4}{5}\text{liters}$

The remaining part of the 1-liter mixture is water:

$\text{Quantity of Water}=1-\frac{4}{5}=\frac{1}{5}\text{liters}$

Therefore, the ratio of water to milk in the mixture is:

$\text{Water}:\text{Milk}=\frac{1}{5}:\frac{4}{5}=1:4$