Question

If $1g$ of gold $10$ carats of fine, $1g$ of gold $11$ carats of fine, $2g$ of gold $12$ carats of fine, and $5g$ of gold $13$ carats of fine be mixed together, find the fineness of the resulting compound

• A. $12.5$
• B. $12\frac{2}{9}$
• C. $12$
• D. $15$

Answer 1

The correct option is B $12\frac{2}{9}$

Total grams of gold $=1+1+2+5=9g$

Required fineness $=10\times \frac{1}{9}+11\times \frac{1}{9}+12\times \frac{2}{9}+13\times \frac{5}{9}$

$=\frac{10}{9}+\frac{11}{9}+\frac{24}{9}+\frac{65}{9}$

$=\frac{110}{9}$

$=12\frac{2}{9}$