In what proportion water must be added to spirit to gain 20% by selling it at the cost price?

Goal: Add water (free) to spirit and sell the mixture at cost price of spirit, gaining 20%.

Let:

• Cost price of spirit = Rs. 1 per litre (assume for simplicity)
• Water has no cost
• Gain desired = 20%

Step 1: Selling price = Cost price = Rs. 1

To get 20% gain, the cost of the entire mixture must be:

Cost of mixture = (100/120) × 1 = Rs. 5/6

Step 2: Let the quantity of spirit be 1 litre

We need to mix water so that cost per litre of the mixture becomes Rs. 5/6

Step 3: Use the formula:

Spirit / Water = (Desired cost of mixture) / (Difference between cost price and desired cost)

Spirit / Water = (5/6) / (1 - 5/6) = (5/6) / (1/6) = 5

So, Spirit : Water = 5 : 1

Final Answer: Water must be added to spirit in the ratio 1 : 5

i.e., add 1 part water to 5 parts spirit