GATE 2026 MT – Question 63
A blast furnace produces hot metal containing 4 wt.% C, 1.5 wt.% Si, and the rest Fe. The only iron input is ore containing 85 wt.% $\mathrm{Fe_2O_3}$ and 15 wt.% gangue consisting of $\mathrm{SiO_2}$ and $\mathrm{Al_2O_3}$. Of all iron by weight, 2% is lost in slag. The ore needed to produce 1000 kg of hot metal is ________ kg. (Rounded off to one decimal place.) Atomic weights: Fe = 56 and O = 16 g/mol.
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Correct answer: 1615.5 to 1625.5
Explanation
The hot metal contains $1000(1-0.04-0.015)=945\ \mathrm{kg}$ Fe. Since 98% of the input iron reaches the metal, the ore must supply $945/0.98\ \mathrm{kg}$ Fe.
The Fe mass fraction in the ore is $0.85[2(56)/(2(56)+3(16))]=0.595$. Thus the ore mass is $945/(0.98\times0.595)=1620.6483\ \mathrm{kg}$, or **1620.6 kg**.