How many kilograms of sugar at Rs. 9/kg must be mixed with 27 kg of sugar at Rs. 7/kg so that selling the mixture at Rs. 9.24/kg yields a 10% gain?

Problem restatement
Two sugars (Rs. 9/kg and Rs. 7/kg) are mixed. The mixture is sold at Rs. 9.24/kg for a 10% profit. Find the required mass of Rs. 9/kg sugar to mix with 27 kg of Rs. 7/kg sugar.

Given data

• SP (mixture) = Rs. 9.24/kg
• Profit% = 10%
• Quantity at Rs. 7/kg = 27 kg
• Quantity at Rs. 9/kg = x kg (unknown)

Concept/Approach
First find the mixture's cost price (CP): CP = SP / (1 + Profit). Then set the weighted average cost equal to this CP and solve for x.

Step-by-step calculation
Mixture CP = 9.24 / 1.10 = 8.40Weighted CP = (9x + 7 × 27) / (x + 27) = 8.409x + 189 = 8.40x + 226.80.60x = 37.8 ⇒ x = 63 kg

Verification/Alternative
Mixture mass = 90 kg; total CP = 8.4 × 90 = 756. Components CP = 63×9 + 27×7 = 567 + 189 = 756 (consistent).

Common pitfalls
Using SP instead of CP for the alligation/average, or forgetting to convert 10% profit into the divisor 1.10.

Final Answer
63 kg