An alloy of Cd and Bi contains 25% Cd. Find the mass of eutectic in 1 kg of alloy if the system contains 40% Cd.

Given: the alloy has 25% Cd (75% Bi). "The system contains 40% Cd" is taken to mean that the eutectic contains 40% Cd (60% Bi), as in the standard version of this problem.

The alloy has less Cd (25%) than the eutectic (40%), so it has excess Bi. On cooling, the excess Bi separates first, and the rest solidifies as eutectic. So the solid alloy is pure Bi + eutectic, and all the Cd is in the eutectic.

Mass of Cd in 1 kg of alloy = 0.25 × 1000 = 250 g.

\( \text{Mass of eutectic} = \dfrac{250 \times 100}{40} = 625\ \text{g} \)

Mass of eutectic = 625 g (0.625 kg), and the free Bi = 375 g.

Check: Bi in the eutectic = 0.60 × 625 = 375 g; 375 + 375 = 750 g = 75% of 1 kg (verified).