An ornament of gold having 75% of gold, is of ............ carat.

$24$carat gold is consider as $100\%$pure gold Given that there is 

$87.5\%$ of gold present in ornament ,So by unitary method.
$100\%$  gold $\to 24$ carat
$1\%$ gold $\to \frac{24}{100}$ carat
 $87.5\%$ gold $\to \frac{24}{100}\times 87.5$ carat
$87.5\%$ gold $\to 21$ carat.
Hence option (A) is correct.