In what percentage water must be added to spirit to gain 25% by selling it at the cost price?

To solve this problem, we can use the concept of the cost price and the selling price. Let's assume that the spirit is initially 100% pure, with no water added.

Now, let's say we want to sell this spirit at the cost price but with a 25% profit. This means that the selling price will be 125% of the cost price.

Let's represent the percentage of water to be added as 'x'. This means that after adding 'x' percentage of water, the spirit will be diluted.

The diluted spirit will now be 100% + 'x'% = (100 + x)%.

According to the problem, the selling price of the diluted spirit should be equal to the cost price. So, we can set up the equation:

Cost Price = Selling Price

100% = (100 + x)%

To solve for 'x', we can cross multiply:

100 * (100 + x) = 100%

Expanding the equation:

10000 + 100x = 10000

Simplifying the equation:

100x = 0

x = 0

This means that no water needs to be added to the spirit in order to gain a 25% profit by selling it at the cost price. The spirit can be sold as it is, without any dilution.