Correct Answer: 1:5
Explanation:
Goal: Add water (free) to spirit and sell the mixture at cost price of spirit, gaining 20%.
Let:
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
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