# A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, then the ratio of gold and copper in alloy C, then the ratio of gold and copper in alloy C will be.

• 15 : 7
• 25 : 9
• 37 : 5
• 49 : 5
$\begin{array}{rl}& \text{Gold in C}\\ & =\left(\frac{7}{9}+\frac{7}{18}\right)\phantom{\rule{thinmathspace}{0ex}}\text{units}\\ & =\frac{\text{7}}{\text{6}}\phantom{\rule{thinmathspace}{0ex}}\text{units}\text{.}\\ & \text{Copper in C}\\ & =\left(\frac{2}{9}+\frac{11}{18}\right)\phantom{\rule{thinmathspace}{0ex}}\text{units}\\ & =\frac{5}{6}\phantom{\rule{thinmathspace}{0ex}}\text{units}\text{.}\\ & \therefore \text{Gold}:\text{Copper}\\ & =\frac{7}{6}:\frac{5}{6}\\ & =7:5.\end{array}$
$\begin{array}{rl}& \text{Gold in C}\\ & =\left(\frac{7}{9}+\frac{7}{18}\right)\phantom{\rule{thinmathspace}{0ex}}\text{units}\\ & =\frac{\text{7}}{\text{6}}\phantom{\rule{thinmathspace}{0ex}}\text{units}\text{.}\\ & \text{Copper in C}\\ & =\left(\frac{2}{9}+\frac{11}{18}\right)\phantom{\rule{thinmathspace}{0ex}}\text{units}\\ & =\frac{5}{6}\phantom{\rule{thinmathspace}{0ex}}\text{units}\text{.}\\ & \therefore \text{Gold}:\text{Copper}\\ & =\frac{7}{6}:\frac{5}{6}\\ & =7:5.\end{array}$