GATE 2018 EC GA Q.7: solution and answer

Official answer: BSource: Official answer key, GATE 2018 EC (IIT Guwahati)

1. Turn each ratio into fractions of the alloy's mass. In A the parts are $2+3=5$, so gold is $\frac{2}{5}$ and copper is $\frac{3}{5}$ of A. In B the parts are $3+7=10$, so gold is $\frac{3}{10}$ and copper is $\frac{7}{10}$ of B.

2. Take the same mass of each alloy. Choosing the LCM of the part totals $5$ and $10$, that is $10\text{kg}$ of each, keeps every quantity a whole number. (Any common mass gives the same final ratio.)

3. Alloy A ($10\text{kg}$): gold $=\frac{2}{5}\times 10=4\text{kg}$, copper $=\frac{3}{5}\times 10=6\text{kg}$.

4. Alloy B ($10\text{kg}$): gold $=\frac{3}{10}\times 10=3\text{kg}$, copper $=\frac{7}{10}\times 10=7\text{kg}$.

5. Melting the two together adds the component masses: gold in C $=4+3=7\text{kg}$ and copper in C $=6+7=13\text{kg}$.

6. So gold : copper in C $=7:13$. Check: $7+13=20\text{kg}$, which is the total mass of the two alloys ($10+10$). The answer is option (B).