How many kilogram 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?

Sure, let's solve this step by step:

Step 1: Let's denote the amount of sugar costing Rs. 9 per kg that must be mixed with 27 kg of sugar costing Rs. 7 per kg as 'x' kg.

Step 2: The cost price of the mixture is the sum of the cost of the two types of sugar. So, the cost price of the mixture is Rs. 9x (for the x kg of sugar costing Rs. 9 per kg) + Rs. 189 (for the 27 kg of sugar costing Rs. 7 per kg).

Step 3: The selling price of the mixture is Rs. 9.24 per (x + 27) kg. Since there is a gain of 10%, the cost price of the mixture is 90% of the selling price.

So, we can set up the following equation:

0.9 * Rs. 9.24 * (x + 27) = Rs. 9x + Rs. 189

Step 4: Simplify the equation to find the value of 'x':

0.9 * 9.24 * x + 0.9 * 9.24 * 27 = 9x + 189

8.316 * x + 224.712 = 9x + 189

Step 5: Solve for 'x':

x = 224.712 - 189 / (9 - 8.316)

x ≈ 35.7 kg

So, approximately 36 kg of sugar costing Rs. 9 per kg must be mixed with the 27 kg of sugar costing Rs. 7 per kg to gain a profit of 10% by selling the mixture at Rs. 9.24 per kg.