GATE 2024 MN – Question 58
Each Cu-grade interval(0.3, 0.4], (0.4, 0.5], (0.5, 0.6], (0.6, 0.7], (0.7, 0.8]% contains 5 million tonnes; other grades have zero tonnage. Concentration costs₹3200/tonne ore, smelting/refining₹10000/tonne copper, and copper sells at₹650000/tonne. Recovery 100%, mining capacity 5 million tonnes/year is the only constraint. Using the profit-maximising mill cutoff, find lifetime copper in million tonnes, to two decimals.
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Correct answer: 9.50 to 10.00
Explanation
Net metal revenue is ₹650000−₹10000 = ₹640000 per tonne copper. With mining capacity the only constraint, the mill cutoff is 3200/640000 = 0.005 = 0.5% Cu. Process the three 5-million-tonne classes above 0.5%. Their midpoint grades are 0.0055, 0.0065 and 0.0075 as fractions. Copper recovered is 5×(0.0055+0.0065+0.0075) = 0.0975 million tonnes, rounding to 0.10. Source-key discrepancy: the official range is 9.50–10.00, consistent with using the percentage numbers without dividing by 100. That range is retained for official grading, but it is not the dimensionally correct metal quantity in the question’s stated units.