GATE 2023 MT – Question 61
The alloy A (given in the phase diagram) is cooled slowly from the liquid state to just below the eutectic temperature. The ratio of weight fractions of pro-eutectic α to eutectic α is ____________ (round off to 1 decimal place).
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Correct answer: 2.3 to 2.7
Explanation
The diagram gives $C_\alpha=15,C_E=50,C_\beta=90$, with alloy composition 30 wt.% Q. Pro-eutectic alpha fraction is $(50-30)/(50-15)=4/7$. Remaining liquid fraction is $3/7$; its eutectic contains alpha fraction $(90-50)/(90-15)=8/15$. Eutectic alpha in the entire alloy is $(3/7)(8/15)=8/35$. The requested ratio is $(4/7)/(8/35)=\boxed{2.5}$.