This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The cost of rice B is 120 per kg. Here's how to calculate it: 1. Interpret the costs: We assume "160 per bag" for rice A implies 160 per kg, as the selling price is per kg and the ratio is by weight. The cost of rice B is given as 'x' per kg. Cost of rice A (C_A) = 160 per kg Cost of rice B (C_B) = x per kg 2. Calculate the total cost price (CP) of the mixture: The rice is mixed in a ratio of 3:1 (A:B). Let's consider 3 kg of A and 1 kg of B for a total of 4 kg of mixture. Cost of 3 kg of A = 3 kg × 160 /kg = 480 Cost of 1 kg of B = 1 kg × x /kg = x Total CP of 4 kg mixture = 480 + x 3. Calculate the total selling price (SP) of the mixture: The mixture is sold at 195 per kg. Total SP of 4 kg mixture = 4 kg × 195 /kg = 780 4. Use the profit percentage to find the cost of B: Profit = 30% The formula relating SP, CP, and profit is: SP = CP × (1 + Profit Percentage / 100) 780 = (480 + x) × (1 + 30/100) 780 = (480 + x) × (1 + 0.30) 780 = (480 + x) × 1.30 5. Solve for x: 480 + x = 780 / 1.30 480 + x = 600 x = 600 - 480 x = 120 Therefore, the cost of B is 120 per kg.