Question

A binary A-B alloy has \( \alpha \) and \( \beta \) phases at equilibrium. The ratio of weight percentages (wt.%) of \( \alpha \) to \( \beta \) is 4. The wt.% of A in \( \alpha \) and \( \beta \) phases is 70 and 20, respectively. The wt.% of B in the alloy is \(\underline{\hspace{2cm}}\) (round off to nearest integer).

Hint:

To calculate the wt.% of B in a binary alloy, use the lever rule and solve for the unknown wt.%.

Answer 1

Correct Answer: 38

Let the wt.% of B in the alloy be \( x \). From the given data, the wt.% of A in the alloy is:
\[ \text{wt.% A} = 100 - x \] Now, use the lever rule for the binary alloy:
\[ \frac{x - 20}{70 - 20} = \frac{4}{5} \] Solving for \( x \), we get:
\[ x = 71. \] Thus, the wt.% of B in the alloy is \( 71 \).