### Find the percentage of pure gold in $10$-carat gold, if 24-carat gold is $100\%$ pure gold.

$41\dfrac { 2 } { 3 }\%$
1. In $10$-carat gold, pure gold is $10$ parts out of $24$ parts. \begin{aligned} \therefore \space \text{Percentage of pure gold in it } = \bigg( \dfrac { 10 } { 24 } \times 100 \bigg)\% = \dfrac { 125 } { 3 } \% = 41\dfrac { 2 } { 3 }\% \end{aligned} Hence, $10$-carat gold is $41\dfrac { 2 } { 3 }\%$ pure.