GATE 2024 MT – Question 61
An 800 g A–B alloy containing 20 wt.% B is held at $T_1$ in the shown phase diagram. The mass of B dissolved in α is ______ g (nearest integer).
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Correct answer: 70 to 70
Explanation
At $T_1$, the tie-line compositions are $C_\alpha=10$ wt.% B and $C_\beta=90$ wt.% B.
The overall composition is 20 wt.% B.
The lever rule gives $f_\alpha=(90-20)/(90-10)=7/8$, so $m_\alpha=800(7/8)=700$ g.
Only 10% of this phase is B: $m_{B\text{ in }\alpha}=0.10(700)=\boxed{70\ \mathrm g}$.