In what ratio must water be mixed with milk to gain 25% by selling the mixture at cost price?

Let's solve this step by step:

Step 1: Let's assume the cost price of 1 litre of milk is $1.

Step 2: If the seller wants to gain 25% by selling the mixture at cost price, it means the cost price of 1 litre of mixture should be $0.75 (because$0.75 is 75% of $1, and selling at this price would mean a 25% gain).

Step 3: The cost price of water is assumed to be $0 (as it's usually negligible compared to milk).

Step 4: Now, we can use the rule of alligation. It's a rule that allows us to find the ratio in which two or more ingredients at a given price must be mixed to produce a mixture of a desired price.

Step 5: According to the rule of alligation, the ratio in which the two ingredients should be mixed is given by (Cost Price of Cheaper - Cost Price of Mixture) : (Cost Price of Mixture - Cost Price of Dearer).

Step 6: Substituting the values, we get (0 - 0.75) : (0.75 - 1) = -0.75 : -0.25.

Step 7: If we remove the negative signs and simplify the ratio, we get 3:1.

So, water and milk should be mixed in the ratio 3:1 to gain 25% by selling the mixture at cost price.