Question

The cut-off grade of copper is 0.45 wt%. A mine has 1 million tonne of waste with a grade of 0.25 wt%. The mine also has stock of high grade ore with a grade of 1.8 wt%. How much of this high grade ore (in million tonne) must be blended with the waste to sell the blended ore at a grade of 0.5 wt%? (Round off to three decimal places)

Answer 1

Correct Answer: 0.191

The problem involves blending a stock of high grade ore with waste to achieve a target grade. Let's analyze the given data: The waste has a grade of 0.25 wt% and weighs 1 million tonnes. The high grade ore has a grade of 1.8 wt%, and we need to blend it to achieve a target grade of 0.5 wt%. Denote x as the mass of high grade ore needed in million tonnes.

Using the formula for the weighted average of grades:

(Grade of Waste)×(Mass of Waste) + (Grade of High Grade Ore)×(Mass of High Grade Ore) = (Target Grade)×(Total Mass)

Substituting the values:

0.25×1 + 1.8×x = 0.5×(1 + x)

Expanding and simplifying this equation:

0.25 + 1.8x = 0.5 + 0.5x

Rearranging terms to isolate x:

1.8x - 0.5x = 0.5 - 0.25

1.3x = 0.25

Solving for x:

x = 0.25 / 1.3 = 0.1923

Rounding to three decimal places, the amount of high grade ore needed is 0.192 million tonnes.