In what ratio sugar of Rs 38 per kg and Rs 30 per kg be mixed with each other so that on selling mixture at Rs 35.2 per kg there will be a profit of 10%?

Step 1: Understand the problem

• We are selling the mixture at Rs. 35.2/kg.
• The profit is 10%, so this is the Selling Price (SP).
• We need to find the Cost Price (CP) of the mixture.

Step 2: Calculate the cost price of the mixture

SP = CP + 10% of CP = 1.10 × CP
So, 35.2 = 1.10 × CP
⇒ CP = 35.2 / 1.10 = Rs. 32/kg

Step 3: Apply alligation rule

• Higher price sugar = Rs. 38/kg
• Lower price sugar = Rs. 30/kg
• Mean price (mixture CP) = Rs. 32/kg

         Rs. 38        Rs. 30
           \           /
            \         /
             \       /
             Rs. 32/kg
             /       \
            /         \
     32 - 30 = 2   38 - 32 = 6

Step 4: Ratio of quantities

Lower price : Higher price = 6 : 2 = 3 : 1

Answer: 3 : 1

The sugar should be mixed in the ratio of 3 : 1 (Rs. 30/kg : Rs. 38/kg) to make 10% profit by selling the mixture at Rs. 35.2 per kg.

This problem demonstrates how to use the alligation method to determine the correct ratio when mixing two items at different prices for a desired selling price and profit margin. It’s a valuable concept for competitive exams and business-related aptitude scenarios.