How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg?

Given:

• Sugar A costs Rs. 9/kg → quantity = x kg
• Sugar B costs Rs. 7/kg → quantity = 27 kg
• Mixture is sold at Rs. 9.24/kg with 10% gain

Step 1: Calculate cost price of the mixture

Since there's a 10% gain on selling price Rs. 9.24/kg:

CP of mixture = 9.24 / 1.10 = Rs. 8.40/kg

Step 2: Use alligation rule

Let A = Rs. 9/kg, B = Rs. 7/kg, Mean = Rs. 8.40/kg

A – Mean = 9 - 8.4 = 0.6 Mean – B = 8.4 - 7 = 1.4

Therefore, the ratio = 1.4 : 0.6 = 14 : 6 = 7 : 3

Step 3: Apply the ratio to the known quantity (sugar B)

3 parts = 27 kg → 1 part = 9 kg

7 parts = 9 × 7 = 63 kg

Answer: 63 kg of sugar costing Rs. 9/kg should be mixed.