A merchant mixes two varieties of oil costing ₹60 per kg and ₹65 per kg. He wants to sell the resulting mixture at ₹68.20 per kg and make a profit of 10%. In what ratio (₹60 oil : ₹65 oil) should the two oils be mixed (assume profit is calculated on the mixture cost price)?

Introduction / Context:
This question combines profit and alligation. First, convert the selling price with profit into the required cost price (mean price) of the mixture. Then use the alligation method to find the mixing ratio between the two oil prices to achieve that mean.

Given Data / Assumptions:

• Oil A price = ₹60 per kg
• Oil B price = ₹65 per kg
• Selling price of mixture = ₹68.20 per kg
• Profit required = 10%
• Cost price of mixture = selling price / (1 + profit)

Concept / Approach:
Find mixture cost price (mean) using profit reversal. Then apply alligation: cheaper : dearer = (dearer - mean) : (mean - cheaper).

Step-by-Step Solution:

Verification / Alternative check:
Check weighted average: (3*60 + 2*65)/(3+2) = (180 + 130)/5 = 310/5 = ₹62. Selling at ₹68.20 gives profit = (68.20-62)/62 *100 = 10%. Verified.

Why Other Options Are Wrong:

Common Pitfalls:
The biggest mistake is using ₹68.20 as the mean directly without removing profit. Another mistake is reversing the alligation differences and flipping the ratio. Always compute CP of mixture first, then apply alligation correctly.

Final Answer:
3:2