An alloy is made by mixing metal A costing Rs 2000 per kg and metal B costing Rs 400 per kg in the ratio A:B = 3:1. What is the total cost (in Rs) of 8 kilograms of this alloy?

Introduction / Context:This is a weighted average cost problem based on mixing ratio. If metals are mixed in ratio 3:1, then out of every 4 equal parts of alloy, 3 parts come from metal A and 1 part comes from metal B. You can either compute the mean cost per kg first and multiply by 8 kg, or directly compute how many kg of each metal are present in 8 kg and then calculate the total cost. Both methods should give the same result.

Given Data / Assumptions:

• Cost of metal A = Rs 2000 per kg
• Cost of metal B = Rs 400 per kg
• Mixing ratio A:B = 3:1
• Total alloy quantity required = 8 kg

Concept / Approach:Method 1 (average cost): Mean cost per kg = (3*2000 + 1*400) / (3+1). Total cost for 8 kg = (mean cost per kg) * 8. Method 2 (component quantities): A quantity = (3/4)*8 and B quantity = (1/4)*8, then compute total cost directly.

Step-by-Step Solution: Total parts = 3 + 1 = 4 Cost of 4 kg equivalent mixture = 3*2000 + 1*400 = 6000 + 400 = 6400 Mean cost per kg = 6400 / 4 = 1600 Total cost for 8 kg = 1600 * 8 = 12800

Verification / Alternative check:Component method: A = (3/4)*8 = 6 kg and B = (1/4)*8 = 2 kg. Cost = 6*2000 + 2*400 = 12000 + 800 = 12800. This matches the average-cost method, confirming correctness.

Why Other Options Are Wrong: 1600 is the cost per kg, not the total for 8 kg. 6400 is the cost corresponding to 4 kg in the 3:1 ratio, not 8 kg. 9800 and 11200 come from incorrect weighting or wrong component quantities.

Common Pitfalls:Forgetting to divide by total parts when finding mean cost, multiplying the 4 kg cost by 8 instead of scaling correctly, or confusing per-kg cost with total cost.

Final Answer:The cost of 8 kg of the alloy is Rs 12800.