In what ratio should sugar costing Rs 38 per kg and sugar costing Rs 30 per kg be mixed so that, on selling the mixture at Rs 35.2 per kg, there is a profit of 10%? (Assume profit percentage is calculated on the cost price of the mixture.)

Introduction / Context:
This question combines two common aptitude ideas: profit percentage and alligation (mixing). The selling price is given, but the mixture must yield a 10% profit, so first you must find the required cost price of the mixture. Only after finding the correct mean cost price can you apply alligation between Rs 38/kg and Rs 30/kg to get the correct mixing ratio. Many wrong answers happen when people treat Rs 35.2 as the cost price directly.

Given Data / Assumptions:

• Cost of sugar type 1 = Rs 38 per kg
• Cost of sugar type 2 = Rs 30 per kg
• Selling price of mixture = Rs 35.2 per kg
• Profit = 10% on cost price

Concept / Approach:
If profit is 10%, then SP = 1.10 * CP. So CP = SP / 1.10. Once the mean cost price (CP of mixture) is known, use alligation: Quantity ratio (dearer : cheaper) = (mean - cheaper) : (dearer - mean).

Step-by-Step Solution:
CP of mixture = 35.2 / 1.10 = 32 Now apply alligation with dearer=38, cheaper=30, mean=32 Required ratio (38 : 30) = (32 - 30) : (38 - 32) = 2 : 6 = 1 : 3

Verification / Alternative check:
Mix 1 kg of Rs 38 with 3 kg of Rs 30. Total cost = 38 + 90 = 128 for 4 kg, so mean CP = 128/4 = 32. Selling at 35.2 gives profit = 35.2 - 32 = 3.2 per kg, which is 3.2/32 = 10%. Verified.

Why Other Options Are Wrong:
13:7 and 9:4 use too much Rs 38 sugar, pushing CP above Rs 32. 3:7 and 2:5 do not produce the exact mean CP of Rs 32 when computed.

Common Pitfalls:
Using 10% of selling price instead of cost price, skipping the CP calculation and treating 35.2 as CP, or reversing the alligation differences incorrectly.

Final Answer:
The sugars should be mixed in the ratio 1:3 (Rs 38/kg : Rs 30/kg).